for @{ 'Forall (λ${ident x}.$Px) }.
notation < "\forall ident x.break term 19 Px" with precedence 20
for @{ 'Forall (λ${ident x}:$tx.$Px) }.
-interpretation "Forall" 'Forall \eta.Px = (Forall _ Px).
+interpretation "Forall" 'Forall \eta.Px = (Forall ? Px).
(* Variables *)
axiom A : CProp.
(* begin a proof: draws the root *)
notation > "'prove' p" non associative with precedence 19
for @{ 'prove $p }.
-interpretation "prove KO" 'prove p = (cast _ _ (show p _)).
-interpretation "prove OK" 'prove p = (show p _).
+interpretation "prove KO" 'prove p = (cast ? ? (show p ?)).
+interpretation "prove OK" 'prove p = (show p ?).
(* Leaves *)
notation < "\infrule (t\atop ⋮) a ?" with precedence 19
interpretation "leaf OK" 'leaf_ok a t = (show a t).
notation < "\infrule (t\atop ⋮) mstyle color #ff0000 (a) ?" with precedence 19
for @{ 'leaf_ko $a $t }.
-interpretation "leaf KO" 'leaf_ko a t = (cast _ _ (show a t)).
+interpretation "leaf KO" 'leaf_ko a t = (cast ? ? (show a t)).
(* discharging *)
notation < "[ a ] \sup mstyle color #ff0000 (H)" with precedence 19
for @{ 'discharge_ko_1 $a $H }.
interpretation "discharge_ko_1" 'discharge_ko_1 a H =
- (show a (cast _ _ (Discharge _ H))).
+ (show a (cast ? ? (Discharge ? H))).
notation < "[ mstyle color #ff0000 (a) ] \sup mstyle color #ff0000 (H)" with precedence 19
for @{ 'discharge_ko_2 $a $H }.
interpretation "discharge_ko_2" 'discharge_ko_2 a H =
- (cast _ _ (show a (cast _ _ (Discharge _ H)))).
+ (cast ? ? (show a (cast ? ? (Discharge ? H)))).
notation < "[ a ] \sup H" with precedence 19
for @{ 'discharge_ok_1 $a $H }.
interpretation "discharge_ok_1" 'discharge_ok_1 a H =
- (show a (Discharge _ H)).
+ (show a (Discharge ? H)).
notation < "[ mstyle color #ff0000 (a) ] \sup H" with precedence 19
for @{ 'discharge_ok_2 $a $H }.
interpretation "discharge_ok_2" 'discharge_ok_2 a H =
- (cast _ _ (show a (Discharge _ H))).
+ (cast ? ? (show a (Discharge ? H))).
notation > "'discharge' [H]" with precedence 19
for @{ 'discharge $H }.
-interpretation "discharge KO" 'discharge H = (cast _ _ (Discharge _ H)).
-interpretation "discharge OK" 'discharge H = (Discharge _ H).
+interpretation "discharge KO" 'discharge H = (cast ? ? (Discharge ? H)).
+interpretation "discharge OK" 'discharge H = (Discharge ? H).
(* ⇒ introduction *)
notation < "\infrule hbox(\emsp b \emsp) ab (mstyle color #ff0000 (⇒\sub\i \emsp) ident H) " with precedence 19
for @{ 'Imply_intro_ko_1 $ab (λ${ident H}:$p.$b) }.
interpretation "Imply_intro_ko_1" 'Imply_intro_ko_1 ab \eta.b =
- (show ab (cast _ _ (Imply_intro _ _ b))).
+ (show ab (cast ? ? (Imply_intro ? ? b))).
notation < "\infrule hbox(\emsp b \emsp) mstyle color #ff0000 (ab) (mstyle color #ff0000 (⇒\sub\i \emsp) ident H) " with precedence 19
for @{ 'Imply_intro_ko_2 $ab (λ${ident H}:$p.$b) }.
interpretation "Imply_intro_ko_2" 'Imply_intro_ko_2 ab \eta.b =
- (cast _ _ (show ab (cast _ _ (Imply_intro _ _ b)))).
+ (cast ? ? (show ab (cast ? ? (Imply_intro ? ? b)))).
notation < "maction (\infrule hbox(\emsp b \emsp) ab (⇒\sub\i \emsp ident H) ) (\vdots)" with precedence 19
for @{ 'Imply_intro_ok_1 $ab (λ${ident H}:$p.$b) }.
interpretation "Imply_intro_ok_1" 'Imply_intro_ok_1 ab \eta.b =
- (show ab (Imply_intro _ _ b)).
+ (show ab (Imply_intro ? ? b)).
notation < "\infrule hbox(\emsp b \emsp) mstyle color #ff0000 (ab) (⇒\sub\i \emsp ident H) " with precedence 19
for @{ 'Imply_intro_ok_2 $ab (λ${ident H}:$p.$b) }.
interpretation "Imply_intro_ok_2" 'Imply_intro_ok_2 ab \eta.b =
- (cast _ _ (show ab (Imply_intro _ _ b))).
+ (cast ? ? (show ab (Imply_intro ? ? b))).
-notation > "⇒_'i' [ident H] term 90 b" with precedence 19
+notation > "⇒#'i' [ident H] term 90 b" with precedence 19
for @{ 'Imply_intro $b (λ${ident H}.show $b ?) }.
+
interpretation "Imply_intro KO" 'Imply_intro b pb =
- (cast _ (Imply unit b) (Imply_intro _ b pb)).
+ (cast ? (Imply unit b) (Imply_intro ? b pb)).
interpretation "Imply_intro OK" 'Imply_intro b pb =
- (Imply_intro _ b pb).
+ (Imply_intro ? b pb).
(* ⇒ elimination *)
notation < "\infrule hbox(\emsp ab \emsp\emsp\emsp a\emsp) b mstyle color #ff0000 (⇒\sub\e) " with precedence 19
for @{ 'Imply_elim_ko_1 $ab $a $b }.
interpretation "Imply_elim_ko_1" 'Imply_elim_ko_1 ab a b =
- (show b (cast _ _ (Imply_elim _ _ (cast _ _ ab) (cast _ _ a)))).
+ (show b (cast ? ? (Imply_elim ? ? (cast ? ? ab) (cast ? ? a)))).
notation < "\infrule hbox(\emsp ab \emsp\emsp\emsp a\emsp) mstyle color #ff0000 (b) mstyle color #ff0000 (⇒\sub\e) " with precedence 19
for @{ 'Imply_elim_ko_2 $ab $a $b }.
interpretation "Imply_elim_ko_2" 'Imply_elim_ko_2 ab a b =
- (cast _ _ (show b (cast _ _ (Imply_elim _ _ (cast _ _ ab) (cast _ _ a))))).
+ (cast ? ? (show b (cast ? ? (Imply_elim ? ? (cast ? ? ab) (cast ? ? a))))).
notation < "maction (\infrule hbox(\emsp ab \emsp\emsp\emsp a\emsp) b (⇒\sub\e) ) (\vdots)" with precedence 19
for @{ 'Imply_elim_ok_1 $ab $a $b }.
interpretation "Imply_elim_ok_1" 'Imply_elim_ok_1 ab a b =
- (show b (Imply_elim _ _ ab a)).
+ (show b (Imply_elim ? ? ab a)).
notation < "\infrule hbox(\emsp ab \emsp\emsp\emsp a\emsp) mstyle color #ff0000 (b) (⇒\sub\e) " with precedence 19
for @{ 'Imply_elim_ok_2 $ab $a $b }.
interpretation "Imply_elim_ok_2" 'Imply_elim_ok_2 ab a b =
- (cast _ _ (show b (Imply_elim _ _ ab a))).
+ (cast ? ? (show b (Imply_elim ? ? ab a))).
-notation > "⇒_'e' term 90 ab term 90 a" with precedence 19
+notation > "⇒#'e' term 90 ab term 90 a" with precedence 19
for @{ 'Imply_elim (show $ab ?) (show $a ?) }.
interpretation "Imply_elim KO" 'Imply_elim ab a =
- (cast _ _ (Imply_elim _ _ (cast (Imply unit unit) _ ab) (cast unit _ a))).
+ (cast ? ? (Imply_elim ? ? (cast (Imply unit unit) ? ab) (cast unit ? a))).
interpretation "Imply_elim OK" 'Imply_elim ab a =
- (Imply_elim _ _ ab a).
+ (Imply_elim ? ? ab a).
(* ∧ introduction *)
notation < "\infrule hbox(\emsp a \emsp\emsp\emsp b \emsp) ab mstyle color #ff0000 (∧\sub\i)" with precedence 19
for @{ 'And_intro_ko_1 $a $b $ab }.
interpretation "And_intro_ko_1" 'And_intro_ko_1 a b ab =
- (show ab (cast _ _ (And_intro _ _ a b))).
+ (show ab (cast ? ? (And_intro ? ? a b))).
notation < "\infrule hbox(\emsp a \emsp\emsp\emsp b \emsp) mstyle color #ff0000 (ab) mstyle color #ff0000 (∧\sub\i)" with precedence 19
for @{ 'And_intro_ko_2 $a $b $ab }.
interpretation "And_intro_ko_2" 'And_intro_ko_2 a b ab =
- (cast _ _ (show ab (cast _ _ (And_intro _ _ a b)))).
+ (cast ? ? (show ab (cast ? ? (And_intro ? ? a b)))).
notation < "maction (\infrule hbox(\emsp a \emsp\emsp\emsp b \emsp) ab (∧\sub\i)) (\vdots)" with precedence 19
for @{ 'And_intro_ok_1 $a $b $ab }.
interpretation "And_intro_ok_1" 'And_intro_ok_1 a b ab =
- (show ab (And_intro _ _ a b)).
+ (show ab (And_intro ? ? a b)).
notation < "\infrule hbox(\emsp a \emsp\emsp\emsp b \emsp) mstyle color #ff0000 (ab) (∧\sub\i)" with precedence 19
for @{ 'And_intro_ok_2 $a $b $ab }.
interpretation "And_intro_ok_2" 'And_intro_ok_2 a b ab =
- (cast _ _ (show ab (And_intro _ _ a b))).
+ (cast ? ? (show ab (And_intro ? ? a b))).
-notation > "∧_'i' term 90 a term 90 b" with precedence 19
+notation > "∧#'i' term 90 a term 90 b" with precedence 19
for @{ 'And_intro (show $a ?) (show $b ?) }.
-interpretation "And_intro KO" 'And_intro a b = (cast _ _ (And_intro _ _ a b)).
-interpretation "And_intro OK" 'And_intro a b = (And_intro _ _ a b).
+interpretation "And_intro KO" 'And_intro a b = (cast ? ? (And_intro ? ? a b)).
+interpretation "And_intro OK" 'And_intro a b = (And_intro ? ? a b).
(* ∧ elimination *)
notation < "\infrule hbox(\emsp ab \emsp) a mstyle color #ff0000 (∧\sub(\e_\l))" with precedence 19
for @{ 'And_elim_l_ko_1 $ab $a }.
interpretation "And_elim_l_ko_1" 'And_elim_l_ko_1 ab a =
- (show a (cast _ _ (And_elim_l _ _ (cast _ _ ab)))).
+ (show a (cast ? ? (And_elim_l ? ? (cast ? ? ab)))).
notation < "\infrule hbox(\emsp ab \emsp) mstyle color #ff0000 (a) mstyle color #ff0000 (∧\sub(\e_\l))" with precedence 19
for @{ 'And_elim_l_ko_2 $ab $a }.
interpretation "And_elim_l_ko_2" 'And_elim_l_ko_2 ab a =
- (cast _ _ (show a (cast _ _ (And_elim_l _ _ (cast _ _ ab))))).
+ (cast ? ? (show a (cast ? ? (And_elim_l ? ? (cast ? ? ab))))).
notation < "maction (\infrule hbox(\emsp ab \emsp) a (∧\sub(\e_\l))) (\vdots)" with precedence 19
for @{ 'And_elim_l_ok_1 $ab $a }.
interpretation "And_elim_l_ok_1" 'And_elim_l_ok_1 ab a =
- (show a (And_elim_l _ _ ab)).
+ (show a (And_elim_l ? ? ab)).
notation < "\infrule hbox(\emsp ab \emsp) mstyle color #ff0000 (a) (∧\sub(\e_\l))" with precedence 19
for @{ 'And_elim_l_ok_2 $ab $a }.
interpretation "And_elim_l_ok_2" 'And_elim_l_ok_2 ab a =
- (cast _ _ (show a (And_elim_l _ _ ab))).
+ (cast ? ? (show a (And_elim_l ? ? ab))).
-notation > "∧_'e_l' term 90 ab" with precedence 19
+notation > "∧#'e_l' term 90 ab" with precedence 19
for @{ 'And_elim_l (show $ab ?) }.
-interpretation "And_elim_l KO" 'And_elim_l a = (cast _ _ (And_elim_l _ _ (cast (And unit unit) _ a))).
-interpretation "And_elim_l OK" 'And_elim_l a = (And_elim_l _ _ a).
+interpretation "And_elim_l KO" 'And_elim_l a = (cast ? ? (And_elim_l ? ? (cast (And unit unit) ? a))).
+interpretation "And_elim_l OK" 'And_elim_l a = (And_elim_l ? ? a).
notation < "\infrule hbox(\emsp ab \emsp) a mstyle color #ff0000 (∧\sub(\e_\r))" with precedence 19
for @{ 'And_elim_r_ko_1 $ab $a }.
interpretation "And_elim_r_ko_1" 'And_elim_r_ko_1 ab a =
- (show a (cast _ _ (And_elim_r _ _ (cast _ _ ab)))).
+ (show a (cast ? ? (And_elim_r ? ? (cast ? ? ab)))).
notation < "\infrule hbox(\emsp ab \emsp) mstyle color #ff0000 (a) mstyle color #ff0000 (∧\sub(\e_\r))" with precedence 19
for @{ 'And_elim_r_ko_2 $ab $a }.
interpretation "And_elim_r_ko_2" 'And_elim_r_ko_2 ab a =
- (cast _ _ (show a (cast _ _ (And_elim_r _ _ (cast _ _ ab))))).
+ (cast ? ? (show a (cast ? ? (And_elim_r ? ? (cast ? ? ab))))).
notation < "maction (\infrule hbox(\emsp ab \emsp) a (∧\sub(\e_\r))) (\vdots)" with precedence 19
for @{ 'And_elim_r_ok_1 $ab $a }.
interpretation "And_elim_r_ok_1" 'And_elim_r_ok_1 ab a =
- (show a (And_elim_r _ _ ab)).
+ (show a (And_elim_r ? ? ab)).
notation < "\infrule hbox(\emsp ab \emsp) mstyle color #ff0000 (a) (∧\sub(\e_\r))" with precedence 19
for @{ 'And_elim_r_ok_2 $ab $a }.
interpretation "And_elim_r_ok_2" 'And_elim_r_ok_2 ab a =
- (cast _ _ (show a (And_elim_r _ _ ab))).
+ (cast ? ? (show a (And_elim_r ? ? ab))).
-notation > "∧_'e_r' term 90 ab" with precedence 19
+notation > "∧#'e_r' term 90 ab" with precedence 19
for @{ 'And_elim_r (show $ab ?) }.
-interpretation "And_elim_r KO" 'And_elim_r a = (cast _ _ (And_elim_r _ _ (cast (And unit unit) _ a))).
-interpretation "And_elim_r OK" 'And_elim_r a = (And_elim_r _ _ a).
+interpretation "And_elim_r KO" 'And_elim_r a = (cast ? ? (And_elim_r ? ? (cast (And unit unit) ? a))).
+interpretation "And_elim_r OK" 'And_elim_r a = (And_elim_r ? ? a).
(* ∨ introduction *)
notation < "\infrule hbox(\emsp a \emsp) ab mstyle color #ff0000 (∨\sub(\i_\l))" with precedence 19
for @{ 'Or_intro_l_ko_1 $a $ab }.
interpretation "Or_intro_l_ko_1" 'Or_intro_l_ko_1 a ab =
- (show ab (cast _ _ (Or_intro_l _ _ a))).
+ (show ab (cast ? ? (Or_intro_l ? ? a))).
notation < "\infrule hbox(\emsp a \emsp) mstyle color #ff0000 (ab) mstyle color #ff0000 (∨\sub(\i_\l))" with precedence 19
for @{ 'Or_intro_l_ko_2 $a $ab }.
interpretation "Or_intro_l_ko_2" 'Or_intro_l_ko_2 a ab =
- (cast _ _ (show ab (cast _ _ (Or_intro_l _ _ a)))).
+ (cast ? ? (show ab (cast ? ? (Or_intro_l ? ? a)))).
notation < "maction (\infrule hbox(\emsp a \emsp) ab (∨\sub(\i_\l))) (\vdots)" with precedence 19
for @{ 'Or_intro_l_ok_1 $a $ab }.
interpretation "Or_intro_l_ok_1" 'Or_intro_l_ok_1 a ab =
- (show ab (Or_intro_l _ _ a)).
+ (show ab (Or_intro_l ? ? a)).
notation < "\infrule hbox(\emsp a \emsp) mstyle color #ff0000 (ab) (∨\sub(\i_\l))" with precedence 19
for @{ 'Or_intro_l_ok_2 $a $ab }.
interpretation "Or_intro_l_ok_2" 'Or_intro_l_ok_2 a ab =
- (cast _ _ (show ab (Or_intro_l _ _ a))).
+ (cast ? ? (show ab (Or_intro_l ? ? a))).
-notation > "∨_'i_l' term 90 a" with precedence 19
+notation > "∨#'i_l' term 90 a" with precedence 19
for @{ 'Or_intro_l (show $a ?) }.
-interpretation "Or_intro_l KO" 'Or_intro_l a = (cast _ (Or _ unit) (Or_intro_l _ _ a)).
-interpretation "Or_intro_l OK" 'Or_intro_l a = (Or_intro_l _ _ a).
+interpretation "Or_intro_l KO" 'Or_intro_l a = (cast ? (Or ? unit) (Or_intro_l ? ? a)).
+interpretation "Or_intro_l OK" 'Or_intro_l a = (Or_intro_l ? ? a).
notation < "\infrule hbox(\emsp a \emsp) ab mstyle color #ff0000 (∨\sub(\i_\r))" with precedence 19
for @{ 'Or_intro_r_ko_1 $a $ab }.
interpretation "Or_intro_r_ko_1" 'Or_intro_r_ko_1 a ab =
- (show ab (cast _ _ (Or_intro_r _ _ a))).
+ (show ab (cast ? ? (Or_intro_r ? ? a))).
notation < "\infrule hbox(\emsp a \emsp) mstyle color #ff0000 (ab) mstyle color #ff0000 (∨\sub(\i_\r))" with precedence 19
for @{ 'Or_intro_r_ko_2 $a $ab }.
interpretation "Or_intro_r_ko_2" 'Or_intro_r_ko_2 a ab =
- (cast _ _ (show ab (cast _ _ (Or_intro_r _ _ a)))).
+ (cast ? ? (show ab (cast ? ? (Or_intro_r ? ? a)))).
notation < "maction (\infrule hbox(\emsp a \emsp) ab (∨\sub(\i_\r))) (\vdots)" with precedence 19
for @{ 'Or_intro_r_ok_1 $a $ab }.
interpretation "Or_intro_r_ok_1" 'Or_intro_r_ok_1 a ab =
- (show ab (Or_intro_r _ _ a)).
+ (show ab (Or_intro_r ? ? a)).
notation < "\infrule hbox(\emsp a \emsp) mstyle color #ff0000 (ab) (∨\sub(\i_\r))" with precedence 19
for @{ 'Or_intro_r_ok_2 $a $ab }.
interpretation "Or_intro_r_ok_2" 'Or_intro_r_ok_2 a ab =
- (cast _ _ (show ab (Or_intro_r _ _ a))).
+ (cast ? ? (show ab (Or_intro_r ? ? a))).
-notation > "∨_'i_r' term 90 a" with precedence 19
+notation > "∨#'i_r' term 90 a" with precedence 19
for @{ 'Or_intro_r (show $a ?) }.
-interpretation "Or_intro_r KO" 'Or_intro_r a = (cast _ (Or unit _) (Or_intro_r _ _ a)).
-interpretation "Or_intro_r OK" 'Or_intro_r a = (Or_intro_r _ _ a).
+interpretation "Or_intro_r KO" 'Or_intro_r a = (cast ? (Or unit ?) (Or_intro_r ? ? a)).
+interpretation "Or_intro_r OK" 'Or_intro_r a = (Or_intro_r ? ? a).
(* ∨ elimination *)
notation < "\infrule hbox(\emsp ab \emsp\emsp\emsp ac \emsp\emsp\emsp bc \emsp) c (mstyle color #ff0000 (∨\sub\e \emsp) ident Ha \emsp ident Hb)" with precedence 19
for @{ 'Or_elim_ko_1 $ab $c (λ${ident Ha}:$ta.$ac) (λ${ident Hb}:$tb.$bc) }.
interpretation "Or_elim_ko_1" 'Or_elim_ko_1 ab c \eta.ac \eta.bc =
- (show c (cast _ _ (Or_elim _ _ _ (cast _ _ ab) (cast _ _ ac) (cast _ _ bc)))).
+ (show c (cast ? ? (Or_elim ? ? ? (cast ? ? ab) (cast ? ? ac) (cast ? ? bc)))).
notation < "\infrule hbox(\emsp ab \emsp\emsp\emsp ac \emsp\emsp\emsp bc \emsp) mstyle color #ff0000 (c) (mstyle color #ff0000 (∨\sub\e) \emsp ident Ha \emsp ident Hb)" with precedence 19
for @{ 'Or_elim_ko_2 $ab (λ${ident Ha}:$ta.$ac) (λ${ident Hb}:$tb.$bc) $c }.
interpretation "Or_elim_ko_2" 'Or_elim_ko_2 ab \eta.ac \eta.bc c =
- (cast _ _ (show c (cast _ _ (Or_elim _ _ _ (cast _ _ ab) (cast _ _ ac) (cast _ _ bc))))).
+ (cast ? ? (show c (cast ? ? (Or_elim ? ? ? (cast ? ? ab) (cast ? ? ac) (cast ? ? bc))))).
notation < "maction (\infrule hbox(\emsp ab \emsp\emsp\emsp ac \emsp\emsp\emsp bc \emsp) c (∨\sub\e \emsp ident Ha \emsp ident Hb)) (\vdots)" with precedence 19
for @{ 'Or_elim_ok_1 $ab (λ${ident Ha}:$ta.$ac) (λ${ident Hb}:$tb.$bc) $c }.
interpretation "Or_elim_ok_1" 'Or_elim_ok_1 ab \eta.ac \eta.bc c =
- (show c (Or_elim _ _ _ ab ac bc)).
+ (show c (Or_elim ? ? ? ab ac bc)).
notation < "\infrule hbox(\emsp ab \emsp\emsp\emsp ac \emsp\emsp\emsp bc \emsp) mstyle color #ff0000 (c) (∨\sub\e \emsp ident Ha \emsp ident Hb)" with precedence 19
for @{ 'Or_elim_ok_2 $ab (λ${ident Ha}:$ta.$ac) (λ${ident Hb}:$tb.$bc) $c }.
interpretation "Or_elim_ok_2" 'Or_elim_ok_2 ab \eta.ac \eta.bc c =
- (cast _ _ (show c (Or_elim _ _ _ ab ac bc))).
+ (cast ? ? (show c (Or_elim ? ? ? ab ac bc))).
definition unit_to ≝ λx:CProp.unit → x.
-notation > "∨_'e' term 90 ab [ident Ha] term 90 cl [ident Hb] term 90 cr" with precedence 19
+notation > "∨#'e' term 90 ab [ident Ha] term 90 cl [ident Hb] term 90 cr" with precedence 19
for @{ 'Or_elim (show $ab ?) (λ${ident Ha}.show $cl ?) (λ${ident Hb}.show $cr ?) }.
interpretation "Or_elim KO" 'Or_elim ab ac bc =
- (cast _ _ (Or_elim _ _ _
- (cast (Or unit unit) _ ab)
- (cast (unit_to unit) (unit_to _) ac)
- (cast (unit_to unit) (unit_to _) bc))).
-interpretation "Or_elim OK" 'Or_elim ab ac bc = (Or_elim _ _ _ ab ac bc).
+ (cast ? ? (Or_elim ? ? ?
+ (cast (Or unit unit) ? ab)
+ (cast (unit_to unit) (unit_to ?) ac)
+ (cast (unit_to unit) (unit_to ?) bc))).
+interpretation "Or_elim OK" 'Or_elim ab ac bc = (Or_elim ? ? ? ab ac bc).
(* ⊤ introduction *)
notation < "\infrule \nbsp ⊤ mstyle color #ff0000 (⊤\sub\i)" with precedence 19
for @{'Top_intro_ko_1}.
interpretation "Top_intro_ko_1" 'Top_intro_ko_1 =
- (show _ (cast _ _ Top_intro)).
+ (show ? (cast ? ? Top_intro)).
notation < "\infrule \nbsp mstyle color #ff0000 (⊤) mstyle color #ff0000 (⊤\sub\i)" with precedence 19
for @{'Top_intro_ko_2}.
interpretation "Top_intro_ko_2" 'Top_intro_ko_2 =
- (cast _ _ (show _ (cast _ _ Top_intro))).
+ (cast ? ? (show ? (cast ? ? Top_intro))).
notation < "maction (\infrule \nbsp ⊤ (⊤\sub\i)) (\vdots)" with precedence 19
for @{'Top_intro_ok_1}.
-interpretation "Top_intro_ok_1" 'Top_intro_ok_1 = (show _ Top_intro).
+interpretation "Top_intro_ok_1" 'Top_intro_ok_1 = (show ? Top_intro).
notation < "maction (\infrule \nbsp ⊤ (⊤\sub\i)) (\vdots)" with precedence 19
for @{'Top_intro_ok_2 }.
-interpretation "Top_intro_ok_2" 'Top_intro_ok_2 = (cast _ _ (show _ Top_intro)).
+interpretation "Top_intro_ok_2" 'Top_intro_ok_2 = (cast ? ? (show ? Top_intro)).
-notation > "⊤_'i'" with precedence 19 for @{ 'Top_intro }.
-interpretation "Top_intro KO" 'Top_intro = (cast _ _ Top_intro).
+notation > "⊤#'i'" with precedence 19 for @{ 'Top_intro }.
+interpretation "Top_intro KO" 'Top_intro = (cast ? ? Top_intro).
interpretation "Top_intro OK" 'Top_intro = Top_intro.
(* ⊥ introduction *)
notation < "\infrule b a mstyle color #ff0000 (⊥\sub\e)" with precedence 19
for @{'Bot_elim_ko_1 $a $b}.
interpretation "Bot_elim_ko_1" 'Bot_elim_ko_1 a b =
- (show a (Bot_elim _ (cast _ _ b))).
+ (show a (Bot_elim ? (cast ? ? b))).
notation < "\infrule b mstyle color #ff0000 (a) mstyle color #ff0000 (⊥\sub\e)" with precedence 19
for @{'Bot_elim_ko_2 $a $b}.
interpretation "Bot_elim_ko_2" 'Bot_elim_ko_2 a b =
- (cast _ _ (show a (Bot_elim _ (cast _ _ b)))).
+ (cast ? ? (show a (Bot_elim ? (cast ? ? b)))).
notation < "maction (\infrule b a (⊥\sub\e)) (\vdots)" with precedence 19
for @{'Bot_elim_ok_1 $a $b}.
interpretation "Bot_elim_ok_1" 'Bot_elim_ok_1 a b =
- (show a (Bot_elim _ b)).
+ (show a (Bot_elim ? b)).
notation < "\infrule b mstyle color #ff0000 (a) (⊥\sub\e)" with precedence 19
for @{'Bot_elim_ok_2 $a $b}.
interpretation "Bot_elim_ok_2" 'Bot_elim_ok_2 a b =
- (cast _ _ (show a (Bot_elim _ b))).
+ (cast ? ? (show a (Bot_elim ? b))).
-notation > "⊥_'e' term 90 b" with precedence 19
+notation > "⊥#'e' term 90 b" with precedence 19
for @{ 'Bot_elim (show $b ?) }.
-interpretation "Bot_elim KO" 'Bot_elim a = (Bot_elim _ (cast _ _ a)).
-interpretation "Bot_elim OK" 'Bot_elim a = (Bot_elim _ a).
+interpretation "Bot_elim KO" 'Bot_elim a = (Bot_elim ? (cast ? ? a)).
+interpretation "Bot_elim OK" 'Bot_elim a = (Bot_elim ? a).
(* ¬ introduction *)
notation < "\infrule hbox(\emsp b \emsp) ab (mstyle color #ff0000 (\lnot\sub(\emsp\i)) \emsp ident H)" with precedence 19
for @{ 'Not_intro_ko_1 $ab (λ${ident H}:$p.$b) }.
interpretation "Not_intro_ko_1" 'Not_intro_ko_1 ab \eta.b =
- (show ab (cast _ _ (Not_intro _ (cast _ _ b)))).
+ (show ab (cast ? ? (Not_intro ? (cast ? ? b)))).
notation < "\infrule hbox(\emsp b \emsp) mstyle color #ff0000 (ab) (mstyle color #ff0000 (\lnot\sub(\emsp\i)) \emsp ident H)" with precedence 19
for @{ 'Not_intro_ko_2 $ab (λ${ident H}:$p.$b) }.
interpretation "Not_intro_ko_2" 'Not_intro_ko_2 ab \eta.b =
- (cast _ _ (show ab (cast _ _ (Not_intro _ (cast _ _ b))))).
+ (cast ? ? (show ab (cast ? ? (Not_intro ? (cast ? ? b))))).
notation < "maction (\infrule hbox(\emsp b \emsp) ab (\lnot\sub(\emsp\i) \emsp ident H) ) (\vdots)" with precedence 19
for @{ 'Not_intro_ok_1 $ab (λ${ident H}:$p.$b) }.
interpretation "Not_intro_ok_1" 'Not_intro_ok_1 ab \eta.b =
- (show ab (Not_intro _ b)).
+ (show ab (Not_intro ? b)).
notation < "\infrule hbox(\emsp b \emsp) mstyle color #ff0000 (ab) (\lnot\sub(\emsp\i) \emsp ident H) " with precedence 19
for @{ 'Not_intro_ok_2 $ab (λ${ident H}:$p.$b) }.
interpretation "Not_intro_ok_2" 'Not_intro_ok_2 ab \eta.b =
- (cast _ _ (show ab (Not_intro _ b))).
+ (cast ? ? (show ab (Not_intro ? b))).
-notation > "¬_'i' [ident H] term 90 b" with precedence 19
+notation > "¬#'i' [ident H] term 90 b" with precedence 19
for @{ 'Not_intro (λ${ident H}.show $b ?) }.
-interpretation "Not_intro KO" 'Not_intro a = (cast _ _ (Not_intro _ (cast _ _ a))).
-interpretation "Not_intro OK" 'Not_intro a = (Not_intro _ a).
+interpretation "Not_intro KO" 'Not_intro a = (cast ? ? (Not_intro ? (cast ? ? a))).
+interpretation "Not_intro OK" 'Not_intro a = (Not_intro ? a).
(* ¬ elimination *)
notation < "\infrule hbox(\emsp ab \emsp\emsp\emsp a\emsp) b mstyle color #ff0000 (\lnot\sub(\emsp\e)) " with precedence 19
for @{ 'Not_elim_ko_1 $ab $a $b }.
interpretation "Not_elim_ko_1" 'Not_elim_ko_1 ab a b =
- (show b (cast _ _ (Not_elim _ (cast _ _ ab) (cast _ _ a)))).
+ (show b (cast ? ? (Not_elim ? (cast ? ? ab) (cast ? ? a)))).
notation < "\infrule hbox(\emsp ab \emsp\emsp\emsp a\emsp) mstyle color #ff0000 (b) mstyle color #ff0000 (\lnot\sub(\emsp\e)) " with precedence 19
for @{ 'Not_elim_ko_2 $ab $a $b }.
interpretation "Not_elim_ko_2" 'Not_elim_ko_2 ab a b =
- (cast _ _ (show b (cast _ _ (Not_elim _ (cast _ _ ab) (cast _ _ a))))).
+ (cast ? ? (show b (cast ? ? (Not_elim ? (cast ? ? ab) (cast ? ? a))))).
notation < "maction (\infrule hbox(\emsp ab \emsp\emsp\emsp a\emsp) b (\lnot\sub(\emsp\e)) ) (\vdots)" with precedence 19
for @{ 'Not_elim_ok_1 $ab $a $b }.
interpretation "Not_elim_ok_1" 'Not_elim_ok_1 ab a b =
- (show b (Not_elim _ ab a)).
+ (show b (Not_elim ? ab a)).
notation < "\infrule hbox(\emsp ab \emsp\emsp\emsp a\emsp) mstyle color #ff0000 (b) (\lnot\sub(\emsp\e)) " with precedence 19
for @{ 'Not_elim_ok_2 $ab $a $b }.
interpretation "Not_elim_ok_2" 'Not_elim_ok_2 ab a b =
- (cast _ _ (show b (Not_elim _ ab a))).
+ (cast ? ? (show b (Not_elim ? ab a))).
-notation > "¬_'e' term 90 ab term 90 a" with precedence 19
+notation > "¬#'e' term 90 ab term 90 a" with precedence 19
for @{ 'Not_elim (show $ab ?) (show $a ?) }.
interpretation "Not_elim KO" 'Not_elim ab a =
- (cast _ _ (Not_elim unit (cast _ _ ab) (cast _ _ a))).
+ (cast ? ? (Not_elim unit (cast ? ? ab) (cast ? ? a))).
interpretation "Not_elim OK" 'Not_elim ab a =
- (Not_elim _ ab a).
+ (Not_elim ? ab a).
(* RAA *)
notation < "\infrule hbox(\emsp Px \emsp) Pn (mstyle color #ff0000 (\RAA) \emsp ident x)" with precedence 19
for @{ 'RAA_ko_1 (λ${ident x}:$tx.$Px) $Pn }.
interpretation "RAA_ko_1" 'RAA_ko_1 Px Pn =
- (show Pn (cast _ _ (Raa _ (cast _ _ Px)))).
+ (show Pn (cast ? ? (Raa ? (cast ? ? Px)))).
notation < "\infrule hbox(\emsp Px \emsp) mstyle color #ff0000 (Pn) (mstyle color #ff0000 (\RAA) \emsp ident x)" with precedence 19
for @{ 'RAA_ko_2 (λ${ident x}:$tx.$Px) $Pn }.
interpretation "RAA_ko_2" 'RAA_ko_2 Px Pn =
- (cast _ _ (show Pn (cast _ _ (Raa _ (cast _ _ Px))))).
+ (cast ? ? (show Pn (cast ? ? (Raa ? (cast ? ? Px))))).
notation < "maction (\infrule hbox(\emsp Px \emsp) Pn (\RAA \emsp ident x)) (\vdots)" with precedence 19
for @{ 'RAA_ok_1 (λ${ident x}:$tx.$Px) $Pn }.
interpretation "RAA_ok_1" 'RAA_ok_1 Px Pn =
- (show Pn (Raa _ Px)).
+ (show Pn (Raa ? Px)).
notation < "\infrule hbox(\emsp Px \emsp) mstyle color #ff0000 (Pn) (\RAA \emsp ident x)" with precedence 19
for @{ 'RAA_ok_2 (λ${ident x}:$tx.$Px) $Pn }.
interpretation "RAA_ok_2" 'RAA_ok_2 Px Pn =
- (cast _ _ (show Pn (Raa _ Px))).
+ (cast ? ? (show Pn (Raa ? Px))).
notation > "'RAA' [ident H] term 90 b" with precedence 19
for @{ 'Raa (λ${ident H}.show $b ?) }.
-interpretation "RAA KO" 'Raa p = (cast _ unit (Raa _ (cast _ (unit_to _) p))).
-interpretation "RAA OK" 'Raa p = (Raa _ p).
+interpretation "RAA KO" 'Raa p = (cast ? unit (Raa ? (cast ? (unit_to ?) p))).
+interpretation "RAA OK" 'Raa p = (Raa ? p).
(* ∃ introduction *)
notation < "\infrule hbox(\emsp Pn \emsp) Px mstyle color #ff0000 (∃\sub\i)" with precedence 19
for @{ 'Exists_intro_ko_1 $Pn $Px }.
interpretation "Exists_intro_ko_1" 'Exists_intro_ko_1 Pn Px =
- (show Px (cast _ _ (Exists_intro _ _ _ (cast _ _ Pn)))).
+ (show Px (cast ? ? (Exists_intro ? ? ? (cast ? ? Pn)))).
notation < "\infrule hbox(\emsp Pn \emsp) mstyle color #ff0000 (Px) mstyle color #ff0000 (∃\sub\i)" with precedence 19
for @{ 'Exists_intro_ko_2 $Pn $Px }.
interpretation "Exists_intro_ko_2" 'Exists_intro_ko_2 Pn Px =
- (cast _ _ (show Px (cast _ _ (Exists_intro _ _ _ (cast _ _ Pn))))).
+ (cast ? ? (show Px (cast ? ? (Exists_intro ? ? ? (cast ? ? Pn))))).
notation < "maction (\infrule hbox(\emsp Pn \emsp) Px (∃\sub\i)) (\vdots)" with precedence 19
for @{ 'Exists_intro_ok_1 $Pn $Px }.
interpretation "Exists_intro_ok_1" 'Exists_intro_ok_1 Pn Px =
- (show Px (Exists_intro _ _ _ Pn)).
+ (show Px (Exists_intro ? ? ? Pn)).
notation < "\infrule hbox(\emsp Pn \emsp) mstyle color #ff0000 (Px) (∃\sub\i)" with precedence 19
for @{ 'Exists_intro_ok_2 $Pn $Px }.
interpretation "Exists_intro_ok_2" 'Exists_intro_ok_2 Pn Px =
- (cast _ _ (show Px (Exists_intro _ _ _ Pn))).
+ (cast ? ? (show Px (Exists_intro ? ? ? Pn))).
-notation >"∃_'i' {term 90 t} term 90 Pt" non associative with precedence 19
+notation >"∃#'i' {term 90 t} term 90 Pt" non associative with precedence 19
for @{'Exists_intro $t (λw.? w) (show $Pt ?)}.
interpretation "Exists_intro KO" 'Exists_intro t P Pt =
- (cast _ _ (Exists_intro sort P t (cast _ _ Pt))).
+ (cast ? ? (Exists_intro sort P t (cast ? ? Pt))).
interpretation "Exists_intro OK" 'Exists_intro t P Pt =
(Exists_intro sort P t Pt).
notation < "\infrule hbox(\emsp ExPx \emsp\emsp\emsp Pc \emsp) c (mstyle color #ff0000 (∃\sub\e) \emsp ident n \emsp ident HPn)" with precedence 19
for @{ 'Exists_elim_ko_1 $ExPx (λ${ident n}:$tn.λ${ident HPn}:$Pn.$Pc) $c }.
interpretation "Exists_elim_ko_1" 'Exists_elim_ko_1 ExPx Pc c =
- (show c (cast _ _ (Exists_elim _ _ _ (cast _ _ ExPx) (cast _ _ Pc)))).
+ (show c (cast ? ? (Exists_elim ? ? ? (cast ? ? ExPx) (cast ? ? Pc)))).
notation < "\infrule hbox(\emsp ExPx \emsp\emsp\emsp Pc \emsp) mstyle color #ff0000 (c) (mstyle color #ff0000 (∃\sub\e) \emsp ident n \emsp ident HPn)" with precedence 19
for @{ 'Exists_elim_ko_2 $ExPx (λ${ident n}:$tn.λ${ident HPn}:$Pn.$Pc) $c }.
interpretation "Exists_elim_ko_2" 'Exists_elim_ko_2 ExPx Pc c =
- (cast _ _ (show c (cast _ _ (Exists_elim _ _ _ (cast _ _ ExPx) (cast _ _ Pc))))).
+ (cast ? ? (show c (cast ? ? (Exists_elim ? ? ? (cast ? ? ExPx) (cast ? ? Pc))))).
notation < "maction (\infrule hbox(\emsp ExPx \emsp\emsp\emsp Pc \emsp) c (∃\sub\e \emsp ident n \emsp ident HPn)) (\vdots)" with precedence 19
for @{ 'Exists_elim_ok_1 $ExPx (λ${ident n}:$tn.λ${ident HPn}:$Pn.$Pc) $c }.
interpretation "Exists_elim_ok_1" 'Exists_elim_ok_1 ExPx Pc c =
- (show c (Exists_elim _ _ _ ExPx Pc)).
+ (show c (Exists_elim ? ? ? ExPx Pc)).
notation < "\infrule hbox(\emsp ExPx \emsp\emsp\emsp Pc \emsp) mstyle color #ff0000 (c) (∃\sub\e \emsp ident n \emsp ident HPn)" with precedence 19
for @{ 'Exists_elim_ok_2 $ExPx (λ${ident n}:$tn.λ${ident HPn}:$Pn.$Pc) $c }.
interpretation "Exists_elim_ok_2" 'Exists_elim_ok_2 ExPx Pc c =
- (cast _ _ (show c (Exists_elim _ _ _ ExPx Pc))).
+ (cast ? ? (show c (Exists_elim ? ? ? ExPx Pc))).
definition ex_concl := λx:sort → CProp.∀y:sort.unit → x y.
definition ex_concl_dummy := ∀y:sort.unit → unit.
definition fake_pred := λx:sort.unit.
-notation >"∃_'e' term 90 ExPt {ident t} [ident H] term 90 c" non associative with precedence 19
+notation >"∃#'e' term 90 ExPt {ident t} [ident H] term 90 c" non associative with precedence 19
for @{'Exists_elim (λx.? x) (show $ExPt ?) (λ${ident t}:sort.λ${ident H}.show $c ?)}.
interpretation "Exists_elim KO" 'Exists_elim P ExPt c =
- (cast _ _ (Exists_elim sort P _
- (cast (Exists _ P) _ ExPt)
- (cast ex_concl_dummy (ex_concl _) c))).
+ (cast ? ? (Exists_elim sort P ?
+ (cast (Exists ? P) ? ExPt)
+ (cast ex_concl_dummy (ex_concl ?) c))).
interpretation "Exists_elim OK" 'Exists_elim P ExPt c =
- (Exists_elim sort P _ ExPt c).
+ (Exists_elim sort P ? ExPt c).
(* ∀ introduction *)
notation < "\infrule hbox(\emsp Px \emsp) Pn (mstyle color #ff0000 (∀\sub\i) \emsp ident x)" with precedence 19
for @{ 'Forall_intro_ko_1 (λ${ident x}:$tx.$Px) $Pn }.
interpretation "Forall_intro_ko_1" 'Forall_intro_ko_1 Px Pn =
- (show Pn (cast _ _ (Forall_intro _ _ (cast _ _ Px)))).
+ (show Pn (cast ? ? (Forall_intro ? ? (cast ? ? Px)))).
notation < "\infrule hbox(\emsp Px \emsp) mstyle color #ff0000(Pn) (mstyle color #ff0000 (∀\sub\i) \emsp ident x)" with precedence 19
for @{ 'Forall_intro_ko_2 (λ${ident x}:$tx.$Px) $Pn }.
interpretation "Forall_intro_ko_2" 'Forall_intro_ko_2 Px Pn =
- (cast _ _ (show Pn (cast _ _ (Forall_intro _ _ (cast _ _ Px))))).
+ (cast ? ? (show Pn (cast ? ? (Forall_intro ? ? (cast ? ? Px))))).
notation < "maction (\infrule hbox(\emsp Px \emsp) Pn (∀\sub\i \emsp ident x)) (\vdots)" with precedence 19
for @{ 'Forall_intro_ok_1 (λ${ident x}:$tx.$Px) $Pn }.
interpretation "Forall_intro_ok_1" 'Forall_intro_ok_1 Px Pn =
- (show Pn (Forall_intro _ _ Px)).
+ (show Pn (Forall_intro ? ? Px)).
notation < "\infrule hbox(\emsp Px \emsp) mstyle color #ff0000 (Pn) (∀\sub\i \emsp ident x)" with precedence 19
for @{ 'Forall_intro_ok_2 (λ${ident x}:$tx.$Px) $Pn }.
interpretation "Forall_intro_ok_2" 'Forall_intro_ok_2 Px Pn =
- (cast _ _ (show Pn (Forall_intro _ _ Px))).
+ (cast ? ? (show Pn (Forall_intro ? ? Px))).
-notation > "∀_'i' {ident y} term 90 Px" non associative with precedence 19
+notation > "∀#'i' {ident y} term 90 Px" non associative with precedence 19
for @{ 'Forall_intro (λ_.?) (λ${ident y}.show $Px ?) }.
interpretation "Forall_intro KO" 'Forall_intro P Px =
- (cast _ _ (Forall_intro sort P (cast _ _ Px))).
+ (cast ? ? (Forall_intro sort P (cast ? ? Px))).
interpretation "Forall_intro OK" 'Forall_intro P Px =
(Forall_intro sort P Px).
notation < "\infrule hbox(\emsp Px \emsp) Pn (mstyle color #ff0000 (∀\sub\e))" with precedence 19
for @{ 'Forall_elim_ko_1 $Px $Pn }.
interpretation "Forall_elim_ko_1" 'Forall_elim_ko_1 Px Pn =
- (show Pn (cast _ _ (Forall_elim _ _ _ (cast _ _ Px)))).
+ (show Pn (cast ? ? (Forall_elim ? ? ? (cast ? ? Px)))).
notation < "\infrule hbox(\emsp Px \emsp) mstyle color #ff0000(Pn) (mstyle color #ff0000 (∀\sub\e))" with precedence 19
for @{ 'Forall_elim_ko_2 $Px $Pn }.
interpretation "Forall_elim_ko_2" 'Forall_elim_ko_2 Px Pn =
- (cast _ _ (show Pn (cast _ _ (Forall_elim _ _ _ (cast _ _ Px))))).
+ (cast ? ? (show Pn (cast ? ? (Forall_elim ? ? ? (cast ? ? Px))))).
notation < "maction (\infrule hbox(\emsp Px \emsp) Pn (∀\sub\e)) (\vdots)" with precedence 19
for @{ 'Forall_elim_ok_1 $Px $Pn }.
interpretation "Forall_elim_ok_1" 'Forall_elim_ok_1 Px Pn =
- (show Pn (Forall_elim _ _ _ Px)).
+ (show Pn (Forall_elim ? ? ? Px)).
notation < "\infrule hbox(\emsp Px \emsp) mstyle color #ff0000 (Pn) (∀\sub\e)" with precedence 19
for @{ 'Forall_elim_ok_2 $Px $Pn }.
interpretation "Forall_elim_ok_2" 'Forall_elim_ok_2 Px Pn =
- (cast _ _ (show Pn (Forall_elim _ _ _ Px))).
+ (cast ? ? (show Pn (Forall_elim ? ? ? Px))).
-notation > "∀_'e' {term 90 t} term 90 Pn" non associative with precedence 19
+notation > "∀#'e' {term 90 t} term 90 Pn" non associative with precedence 19
for @{ 'Forall_elim (λ_.?) $t (show $Pn ?) }.
interpretation "Forall_elim KO" 'Forall_elim P t Px =
- (cast _ unit (Forall_elim sort P t (cast _ _ Px))).
+ (cast ? unit (Forall_elim sort P t (cast ? ? Px))).
interpretation "Forall_elim OK" 'Forall_elim P t Px =
(Forall_elim sort P t Px).
(* already proved lemma *)
-definition hide_args : ∀A:Type.∀a:A.A := λA:Type.λa:A.a.
+definition hide_args : ∀A:Type.A→A := λA:Type.λa:A.a.
notation < "t" non associative with precedence 90 for @{'hide_args $t}.
-interpretation "hide 0 args" 'hide_args t = (hide_args _ t).
-interpretation "hide 1 args" 'hide_args t = (hide_args _ t _).
-interpretation "hide 2 args" 'hide_args t = (hide_args _ t _ _).
-interpretation "hide 3 args" 'hide_args t = (hide_args _ t _ _ _).
-interpretation "hide 4 args" 'hide_args t = (hide_args _ t _ _ _ _).
-interpretation "hide 5 args" 'hide_args t = (hide_args _ t _ _ _ _ _).
-interpretation "hide 6 args" 'hide_args t = (hide_args _ t _ _ _ _ _ _).
-interpretation "hide 7 args" 'hide_args t = (hide_args _ t _ _ _ _ _ _ _).
+interpretation "hide 0 args" 'hide_args t = (hide_args ? t).
+interpretation "hide 1 args" 'hide_args t = (hide_args ? t ?).
+interpretation "hide 2 args" 'hide_args t = (hide_args ? t ? ?).
+interpretation "hide 3 args" 'hide_args t = (hide_args ? t ? ? ?).
+interpretation "hide 4 args" 'hide_args t = (hide_args ? t ? ? ? ?).
+interpretation "hide 5 args" 'hide_args t = (hide_args ? t ? ? ? ? ?).
+interpretation "hide 6 args" 'hide_args t = (hide_args ? t ? ? ? ? ? ?).
+interpretation "hide 7 args" 'hide_args t = (hide_args ? t ? ? ? ? ? ? ?).
(* more args crashes the pattern matcher *)
non associative with precedence 19
for @{ 'lemma_ko_1 $p ($H : $_) }.
interpretation "lemma_ko_1" 'lemma_ko_1 p H =
- (show p (cast _ _ (Lemma _ (cast _ _ H)))).
+ (show p (cast ? ? (Lemma ? (cast ? ? H)))).
notation < "\infrule
(\infrule
non associative with precedence 19
for @{ 'lemma_ko_2 $p ($H : $_) }.
interpretation "lemma_ko_2" 'lemma_ko_2 p H =
- (cast _ _ (show p (cast _ _
- (Lemma _ (cast _ _ H))))).
+ (cast ? ? (show p (cast ? ?
+ (Lemma ? (cast ? ? H))))).
notation < "\infrule
non associative with precedence 19
for @{ 'lemma_ok_1 $p ($H : $_) }.
interpretation "lemma_ok_1" 'lemma_ok_1 p H =
- (show p (Lemma _ H)).
+ (show p (Lemma ? H)).
notation < "\infrule
(\infrule
non associative with precedence 19
for @{ 'lemma_ok_2 $p ($H : $_) }.
interpretation "lemma_ok_2" 'lemma_ok_2 p H =
- (cast _ _ (show p (Lemma _ H))).
+ (cast ? ? (show p (Lemma ? H))).
notation > "'lem' 0 term 90 l" non associative with precedence 19
for @{ 'Lemma (hide_args ? $l : ?) }.
interpretation "lemma KO" 'Lemma l =
- (cast _ _ (Lemma unit (cast unit _ l))).
-interpretation "lemma OK" 'Lemma l = (Lemma _ l).
+ (cast ? ? (Lemma unit (cast unit ? l))).
+interpretation "lemma OK" 'Lemma l = (Lemma ? l).
(* already proved lemma, 1 assumption *)
non associative with precedence 19
for @{ 'lemma1_ko_1 $a $p ($H : $_) }.
interpretation "lemma1_ko_1" 'lemma1_ko_1 a p H =
- (show p (cast _ _ (Lemma1 _ _ (cast _ _ H) (cast _ _ a)))).
+ (show p (cast ? ? (Lemma1 ? ? (cast ? ? H) (cast ? ? a)))).
notation < "\infrule
(\infrule
non associative with precedence 19
for @{ 'lemma1_ko_2 $a $p ($H : $_) }.
interpretation "lemma1_ko_2" 'lemma1_ko_2 a p H =
- (cast _ _ (show p (cast _ _
- (Lemma1 _ _ (cast _ _ H) (cast _ _ a))))).
+ (cast ? ? (show p (cast ? ?
+ (Lemma1 ? ? (cast ? ? H) (cast ? ? a))))).
notation < "\infrule
non associative with precedence 19
for @{ 'lemma1_ok_1 $a $p ($H : $_) }.
interpretation "lemma1_ok_1" 'lemma1_ok_1 a p H =
- (show p (Lemma1 _ _ H a)).
+ (show p (Lemma1 ? ? H a)).
notation < "\infrule
(\infrule
non associative with precedence 19
for @{ 'lemma1_ok_2 $a $p ($H : $_) }.
interpretation "lemma1_ok_2" 'lemma1_ok_2 a p H =
- (cast _ _ (show p (Lemma1 _ _ H a))).
+ (cast ? ? (show p (Lemma1 ? ? H a))).
notation > "'lem' 1 term 90 l term 90 p" non associative with precedence 19
for @{ 'Lemma1 (hide_args ? $l : ?) (show $p ?) }.
interpretation "lemma 1 KO" 'Lemma1 l p =
- (cast _ _ (Lemma1 unit unit (cast (Imply unit unit) _ l) (cast unit _ p))).
-interpretation "lemma 1 OK" 'Lemma1 l p = (Lemma1 _ _ l p).
+ (cast ? ? (Lemma1 unit unit (cast (Imply unit unit) ? l) (cast unit ? p))).
+interpretation "lemma 1 OK" 'Lemma1 l p = (Lemma1 ? ? l p).
(* already proved lemma, 2 assumptions *)
definition Lemma2 : ΠA,B,C. (A ⇒ B ⇒ C) → A → B → C ≝
non associative with precedence 19
for @{ 'lemma2_ko_1 $a $b $p ($H : $_) }.
interpretation "lemma2_ko_1" 'lemma2_ko_1 a b p H =
- (show p (cast _ _ (Lemma2 _ _ _ (cast _ _ H) (cast _ _ a) (cast _ _ b)))).
+ (show p (cast ? ? (Lemma2 ? ? ? (cast ? ? H) (cast ? ? a) (cast ? ? b)))).
notation < "\infrule
(\infrule
non associative with precedence 19
for @{ 'lemma2_ko_2 $a $b $p ($H : $_) }.
interpretation "lemma2_ko_2" 'lemma2_ko_2 a b p H =
- (cast _ _ (show p (cast _ _
- (Lemma2 _ _ _ (cast _ _ H) (cast _ _ a) (cast _ _ b))))).
+ (cast ? ? (show p (cast ? ?
+ (Lemma2 ? ? ? (cast ? ? H) (cast ? ? a) (cast ? ? b))))).
notation < "\infrule
non associative with precedence 19
for @{ 'lemma2_ok_1 $a $b $p ($H : $_) }.
interpretation "lemma2_ok_1" 'lemma2_ok_1 a b p H =
- (show p (Lemma2 _ _ _ H a b)).
+ (show p (Lemma2 ? ? ? H a b)).
notation < "\infrule
(\infrule
non associative with precedence 19
for @{ 'lemma2_ok_2 $a $b $p ($H : $_) }.
interpretation "lemma2_ok_2" 'lemma2_ok_2 a b p H =
- (cast _ _ (show p (Lemma2 _ _ _ H a b))).
+ (cast ? ? (show p (Lemma2 ? ? ? H a b))).
notation > "'lem' 2 term 90 l term 90 p term 90 q" non associative with precedence 19
for @{ 'Lemma2 (hide_args ? $l : ?) (show $p ?) (show $q ?) }.
interpretation "lemma 2 KO" 'Lemma2 l p q =
- (cast _ _ (Lemma2 unit unit unit (cast (Imply unit (Imply unit unit)) _ l) (cast unit _ p) (cast unit _ q))).
-interpretation "lemma 2 OK" 'Lemma2 l p q = (Lemma2 _ _ _ l p q).
+ (cast ? ? (Lemma2 unit unit unit (cast (Imply unit (Imply unit unit)) ? l) (cast unit ? p) (cast unit ? q))).
+interpretation "lemma 2 OK" 'Lemma2 l p q = (Lemma2 ? ? ? l p q).
(* already proved lemma, 3 assumptions *)
definition Lemma3 : ΠA,B,C,D. (A ⇒ B ⇒ C ⇒ D) → A → B → C → D ≝
non associative with precedence 19
for @{ 'lemma3_ko_1 $a $b $c $p ($H : $_) }.
interpretation "lemma3_ko_1" 'lemma3_ko_1 a b c p H =
- (show p (cast _ _
- (Lemma3 _ _ _ _ (cast _ _ H) (cast _ _ a) (cast _ _ b) (cast _ _ c)))).
+ (show p (cast ? ?
+ (Lemma3 ? ? ? ? (cast ? ? H) (cast ? ? a) (cast ? ? b) (cast ? ? c)))).
notation < "\infrule
(\infrule
non associative with precedence 19
for @{ 'lemma3_ko_2 $a $b $c $p ($H : $_) }.
interpretation "lemma3_ko_2" 'lemma3_ko_2 a b c p H =
- (cast _ _ (show p (cast _ _
- (Lemma3 _ _ _ _ (cast _ _ H) (cast _ _ a) (cast _ _ b) (cast _ _ c))))).
+ (cast ? ? (show p (cast ? ?
+ (Lemma3 ? ? ? ? (cast ? ? H) (cast ? ? a) (cast ? ? b) (cast ? ? c))))).
notation < "\infrule
non associative with precedence 19
for @{ 'lemma3_ok_1 $a $b $c $p ($H : $_) }.
interpretation "lemma3_ok_1" 'lemma3_ok_1 a b c p H =
- (show p (Lemma3 _ _ _ _ H a b c)).
+ (show p (Lemma3 ? ? ? ? H a b c)).
notation < "\infrule
(\infrule
non associative with precedence 19
for @{ 'lemma3_ok_2 $a $b $c $p ($H : $_) }.
interpretation "lemma3_ok_2" 'lemma3_ok_2 a b c p H =
- (cast _ _ (show p (Lemma3 _ _ _ _ H a b c))).
+ (cast ? ? (show p (Lemma3 ? ? ? ? H a b c))).
notation > "'lem' 3 term 90 l term 90 p term 90 q term 90 r" non associative with precedence 19
for @{ 'Lemma3 (hide_args ? $l : ?) (show $p ?) (show $q ?) (show $r ?) }.
interpretation "lemma 3 KO" 'Lemma3 l p q r =
- (cast _ _ (Lemma3 unit unit unit unit (cast (Imply unit (Imply unit (Imply unit unit))) _ l) (cast unit _ p) (cast unit _ q) (cast unit _ r))).
-interpretation "lemma 3 OK" 'Lemma3 l p q r = (Lemma3 _ _ _ _ l p q r).
+ (cast ? ? (Lemma3 unit unit unit unit (cast (Imply unit (Imply unit (Imply unit unit))) ? l) (cast unit ? p) (cast unit ? q) (cast unit ? r))).
+interpretation "lemma 3 OK" 'Lemma3 l p q r = (Lemma3 ? ? ? ? l p q r).
projects / helm.git / blobdiff