X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matitaB%2Fmatita%2Flib%2Fbasics%2Flogic.ma;h=374947b7d96bbfedaaea2925d26e8a26b37db54a;hb=6c52017b15171aa20ddfd01c1bbf3cc22a86c81c;hp=34299aff0072b77a9a78c75c23d7ed8e3bccf889;hpb=42680d47c033d751738fd0f84af7b45b2a91a5b8;p=helm.git
diff --git a/matitaB/matita/lib/basics/logic.ma b/matitaB/matita/lib/basics/logic.ma
index 34299aff0..374947b7d 100644
--- a/matitaB/matita/lib/basics/logic.ma
+++ b/matitaB/matita/lib/basics/logic.ma
@@ -20,43 +20,43 @@ inductive eq (A:Type[1]) (x:A) : A â Prop â
interpretation "leibnitz's equality" 'eq t x y = (eq t x y).
lemma eq_rect_r:
- âA.âa,x.âp:eq ? x a.âP:
- âx:A. x = a â Type[2]. P a (refl A a) â P x p.
+ âA.âa,x.âp:A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A ? x a.âP:
+ âx:A. x A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A a â Type[2]. P a (refl A a) â P x p.
#A #a #x #p (cases p) // qed.
lemma eq_ind_r :
- âA.âa.âP: âx:A. x = a â Prop. P a (refl A a) â
- âx.âp:eq ? x a.P x p.
- #A #a #P #p #x0 #p0; @(eq_rect_r ? ? ? p0) //; qed.
+ âA.âa.âP: âx:A. x A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A a â Prop. P a (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A A a) â
+ âx.âp:A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A ? x a.P x p.
+ #A #a #P #p #x0 #p0; @(A href="cic:/matita/basics/logic/eq_rect_r.def(1)"eq_rect_r/A ? ? ? p0) //; qed.
lemma eq_rect_Type2_r:
- âA.âa.âP: âx:A. eq ? x a â Type[2]. P a (refl A a) â
- âx.âp:eq ? x a.P x p.
+ âA.âa.âP: âx:A. A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A ? x a â Type[2]. P a (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A A a) â
+ âx.âp:A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A ? x a.P x p.
#A #a #P #H #x #p (generalize in match H) (generalize in match P)
cases p; //; qed.
-theorem rewrite_l: âA:Type[1].âx.âP:A â Type[1]. P x â ây. x = y â P y.
+theorem rewrite_l: âA:Type[1].âx.âP:A â Type[1]. P x â ây. x A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A y â P y.
#A #x #P #Hx #y #Heq (cases Heq); //; qed.
-theorem sym_eq: âA.âx,y:A. x = y â y = x.
-#A #x #y #Heq @(rewrite_l A x (λz.z=x)); //; qed.
+theorem sym_eq: âA.âx,y:A. x A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A y â y A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A x.
+#A #x #y #Heq @(A href="cic:/matita/basics/logic/rewrite_l.def(1)"rewrite_l/A A x (λz.zA title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/Ax)); //; qed.
-theorem rewrite_r: âA:Type[1].âx.âP:A â Type[1]. P x â ây. y = x â P y.
-#A #x #P #Hx #y #Heq (cases (sym_eq ? ? ? Heq)); //; qed.
+theorem rewrite_r: âA:Type[1].âx.âP:A â Type[1]. P x â ây. y A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A x â P y.
+#A #x #P #Hx #y #Heq (cases (A href="cic:/matita/basics/logic/sym_eq.def(2)"sym_eq/A ? ? ? Heq)); //; qed.
-theorem eq_coerc: âA,B:Type[0].Aâ(A=B)âB.
+theorem eq_coerc: âA,B:Type[0].Aâ(AA title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/AB)âB.
#A #B #Ha #Heq (elim Heq); //; qed.
-theorem trans_eq : âA.âx,y,z:A. x = y â y = z â x = z.
+theorem trans_eq : âA.âx,y,z:A. x A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A y â y A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A z â x A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A z.
#A #x #y #z #H1 #H2 >H1; //; qed.
-theorem eq_f: âA,B.âf:AâB.âx,y:A. x=y â f x = f y.
+theorem eq_f: âA,B.âf:AâB.âx,y:A. xA title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/Ay â f x A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A f y.
#A #B #f #x #y #H >H; //; qed.
(* deleterio per auto? *)
theorem eq_f2: âA,B,C.âf:AâBâC.
-âx1,x2:A.ây1,y2:B. x1=x2 â y1=y2 â f x1 y1 = f x2 y2.
-#A #B #C #f #x1 #x2 #y1 #y2 #E1 #E2 >E1; >E2; //; qed.
+âx1,x2:A.ây1,y2:B. x1A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/Ax2 â y1A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/Ay2 â f x1 y1 A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A f x2 y2.
+#A #B #C #f #x1 #x2 #y1 #y2 #E1 #E2 E1; E2; //; qed.
(* hint to genereric equality
definition eq_equality: equality â
@@ -80,12 +80,12 @@ inductive False: Prop â .
λA. A â False. *)
inductive Not (A:Prop): Prop â
-nmk: (A â False) â Not A.
+nmk: (A â A href="cic:/matita/basics/logic/False.ind(1,0,0)"False/A) â Not A.
interpretation "logical not" 'not x = (Not x).
-theorem absurd : âA:Prop. A â ¬A â False.
+theorem absurd : âA:Prop. A â A title="logical not" href="cic:/fakeuri.def(1)"¬/AA â A href="cic:/matita/basics/logic/False.ind(1,0,0)"False/A.
#A #H #Hn (elim Hn); /2/; qed.
(*
@@ -93,13 +93,13 @@ ntheorem absurd : â A,C:Prop. A â ¬A â C.
#A; #C; #H; #Hn; nelim (Hn H).
nqed. *)
-theorem not_to_not : âA,B:Prop. (A â B) â ¬B â¬A.
+theorem not_to_not : âA,B:Prop. (A â B) â A title="logical not" href="cic:/fakeuri.def(1)"¬/AB âA title="logical not" href="cic:/fakeuri.def(1)"¬/AA.
/4/; qed.
(* inequality *)
interpretation "leibnitz's non-equality" 'neq t x y = (Not (eq t x y)).
-theorem sym_not_eq: âA.âx,y:A. x â y â y â x.
+theorem sym_not_eq: âA.âx,y:A. x A title="leibnitz's non-equality" href="cic:/fakeuri.def(1)"â /A y â y A title="leibnitz's non-equality" href="cic:/fakeuri.def(1)"â /A x.
/3/; qed.
(* and *)
@@ -108,10 +108,10 @@ inductive And (A,B:Prop) : Prop â
interpretation "logical and" 'and x y = (And x y).
-theorem proj1: âA,B:Prop. A ⧠B â A.
+theorem proj1: âA,B:Prop. A A title="logical and" href="cic:/fakeuri.def(1)"â§/A B â A.
#A #B #AB (elim AB) //; qed.
-theorem proj2: â A,B:Prop. A ⧠B â B.
+theorem proj2: â A,B:Prop. A A title="logical and" href="cic:/fakeuri.def(1)"â§/A B â B.
#A #B #AB (elim AB) //; qed.
(* or *)
@@ -122,7 +122,7 @@ inductive Or (A,B:Prop) : Prop â
interpretation "logical or" 'or x y = (Or x y).
definition decidable : Prop â Prop â
-λ A:Prop. A ⨠¬ A.
+λ A:Prop. A A title="logical or" href="cic:/fakeuri.def(1)"â¨/A A title="logical not" href="cic:/fakeuri.def(1)"¬/A A.
(* exists *)
inductive ex (A:Type[0]) (P:A â Prop) : Prop â
@@ -135,7 +135,7 @@ inductive ex2 (A:Type[0]) (P,Q:A âProp) : Prop â
(* iff *)
definition iff :=
- λ A,B. (A â B) ⧠(B â A).
+ λ A,B. (A â B) A title="logical and" href="cic:/fakeuri.def(1)"â§/A (B â A).
interpretation "iff" 'iff a b = (iff a b).
@@ -143,84 +143,84 @@ interpretation "iff" 'iff a b = (iff a b).
definition R0 â λT:Type[0].λt:T.t.
-definition R1 â eq_rect_Type0.
+definition R1 â A href="cic:/matita/basics/logic/eq_rect_Type0.fix(0,5,1)"eq_rect_Type0/A.
(* useless stuff *)
definition R2 :
âT0:Type[0].
âa0:T0.
- âT1:âx0:T0. a0=x0 â Type[0].
- âa1:T1 a0 (refl ? a0).
- âT2:âx0:T0. âp0:a0=x0. âx1:T1 x0 p0. R1 ?? T1 a1 ? p0 = x1 â Type[0].
- âa2:T2 a0 (refl ? a0) a1 (refl ? a1).
+ âT1:âx0:T0. a0A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/Ax0 â Type[0].
+ âa1:T1 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A ? a0).
+ âT2:âx0:T0. âp0:a0A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/Ax0. âx1:T1 x0 p0. A href="cic:/matita/basics/logic/R1.def(2)"R1/A ?? T1 a1 ? p0 A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A x1 â Type[0].
+ âa2:T2 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A ? a0) a1 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A ? a1).
âb0:T0.
- âe0:a0 = b0.
+ âe0:a0 A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A b0.
âb1: T1 b0 e0.
- âe1:R1 ?? T1 a1 ? e0 = b1.
+ âe1:A href="cic:/matita/basics/logic/R1.def(2)"R1/A ?? T1 a1 ? e0 A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A b1.
T2 b0 e0 b1 e1.
#T0 #a0 #T1 #a1 #T2 #a2 #b0 #e0 #b1 #e1
-@(eq_rect_Type0 ????? e1)
-@(R1 ?? ? ?? e0)
+@(A href="cic:/matita/basics/logic/eq_rect_Type0.fix(0,5,1)"eq_rect_Type0/A ????? e1)
+@(A href="cic:/matita/basics/logic/R1.def(2)"R1/A ?? ? ?? e0)
@a2
qed.
definition R3 :
âT0:Type[0].
âa0:T0.
- âT1:âx0:T0. a0=x0 â Type[0].
- âa1:T1 a0 (refl ? a0).
- âT2:âx0:T0. âp0:a0=x0. âx1:T1 x0 p0. R1 ?? T1 a1 ? p0 = x1 â Type[0].
- âa2:T2 a0 (refl ? a0) a1 (refl ? a1).
- âT3:âx0:T0. âp0:a0=x0. âx1:T1 x0 p0.âp1:R1 ?? T1 a1 ? p0 = x1.
- âx2:T2 x0 p0 x1 p1.R2 ???? T2 a2 x0 p0 ? p1 = x2 â Type[0].
- âa3:T3 a0 (refl ? a0) a1 (refl ? a1) a2 (refl ? a2).
+ âT1:âx0:T0. a0A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/Ax0 â Type[0].
+ âa1:T1 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A ? a0).
+ âT2:âx0:T0. âp0:a0A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/Ax0. âx1:T1 x0 p0. A href="cic:/matita/basics/logic/R1.def(2)"R1/A ?? T1 a1 ? p0 A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A x1 â Type[0].
+ âa2:T2 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A ? a0) a1 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A ? a1).
+ âT3:âx0:T0. âp0:a0A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/Ax0. âx1:T1 x0 p0.âp1:A href="cic:/matita/basics/logic/R1.def(2)"R1/A ?? T1 a1 ? p0 A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A x1.
+ âx2:T2 x0 p0 x1 p1.A href="cic:/matita/basics/logic/R2.def(3)"R2/A ???? T2 a2 x0 p0 ? p1 A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A x2 â Type[0].
+ âa3:T3 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A ? a0) a1 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A ? a1) a2 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A ? a2).
âb0:T0.
- âe0:a0 = b0.
+ âe0:a0 A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A b0.
âb1: T1 b0 e0.
- âe1:R1 ?? T1 a1 ? e0 = b1.
+ âe1:A href="cic:/matita/basics/logic/R1.def(2)"R1/A ?? T1 a1 ? e0 A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A b1.
âb2: T2 b0 e0 b1 e1.
- âe2:R2 ???? T2 a2 b0 e0 ? e1 = b2.
+ âe2:A href="cic:/matita/basics/logic/R2.def(3)"R2/A ???? T2 a2 b0 e0 ? e1 A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A b2.
T3 b0 e0 b1 e1 b2 e2.
#T0 #a0 #T1 #a1 #T2 #a2 #T3 #a3 #b0 #e0 #b1 #e1 #b2 #e2
-@(eq_rect_Type0 ????? e2)
-@(R2 ?? ? ???? e0 ? e1)
+@(A href="cic:/matita/basics/logic/eq_rect_Type0.fix(0,5,1)"eq_rect_Type0/A ????? e2)
+@(A href="cic:/matita/basics/logic/R2.def(3)"R2/A ?? ? ???? e0 ? e1)
@a3
qed.
definition R4 :
âT0:Type[0].
âa0:T0.
- âT1:âx0:T0. eq T0 a0 x0 â Type[0].
- âa1:T1 a0 (refl T0 a0).
- âT2:âx0:T0. âp0:eq (T0 â¦) a0 x0. âx1:T1 x0 p0.eq (T1 â¦) (R1 T0 a0 T1 a1 x0 p0) x1 â Type[0].
- âa2:T2 a0 (refl T0 a0) a1 (refl (T1 a0 (refl T0 a0)) a1).
- âT3:âx0:T0. âp0:eq (T0 â¦) a0 x0. âx1:T1 x0 p0.âp1:eq (T1 â¦) (R1 T0 a0 T1 a1 x0 p0) x1.
- âx2:T2 x0 p0 x1 p1.eq (T2 â¦) (R2 T0 a0 T1 a1 T2 a2 x0 p0 x1 p1) x2 â Type[0].
- âa3:T3 a0 (refl T0 a0) a1 (refl (T1 a0 (refl T0 a0)) a1)
- a2 (refl (T2 a0 (refl T0 a0) a1 (refl (T1 a0 (refl T0 a0)) a1)) a2).
- âT4:âx0:T0. âp0:eq (T0 â¦) a0 x0. âx1:T1 x0 p0.âp1:eq (T1 â¦) (R1 T0 a0 T1 a1 x0 p0) x1.
- âx2:T2 x0 p0 x1 p1.âp2:eq (T2 â¦) (R2 T0 a0 T1 a1 T2 a2 x0 p0 x1 p1) x2.
- âx3:T3 x0 p0 x1 p1 x2 p2.âp3:eq (T3 â¦) (R3 T0 a0 T1 a1 T2 a2 T3 a3 x0 p0 x1 p1 x2 p2) x3.
+ âT1:âx0:T0. A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A T0 a0 x0 â Type[0].
+ âa1:T1 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A T0 a0).
+ âT2:âx0:T0. âp0:A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A (T0 â¦) a0 x0. âx1:T1 x0 p0.A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A (T1 â¦) (A href="cic:/matita/basics/logic/R1.def(2)"R1/A T0 a0 T1 a1 x0 p0) x1 â Type[0].
+ âa2:T2 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A T0 a0) a1 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A (T1 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A T0 a0)) a1).
+ âT3:âx0:T0. âp0:A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A (T0 â¦) a0 x0. âx1:T1 x0 p0.âp1:A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A (T1 â¦) (A href="cic:/matita/basics/logic/R1.def(2)"R1/A T0 a0 T1 a1 x0 p0) x1.
+ âx2:T2 x0 p0 x1 p1.A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A (T2 â¦) (A href="cic:/matita/basics/logic/R2.def(3)"R2/A T0 a0 T1 a1 T2 a2 x0 p0 x1 p1) x2 â Type[0].
+ âa3:T3 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A T0 a0) a1 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A (T1 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A T0 a0)) a1)
+ a2 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A (T2 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A T0 a0) a1 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A (T1 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A T0 a0)) a1)) a2).
+ âT4:âx0:T0. âp0:A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A (T0 â¦) a0 x0. âx1:T1 x0 p0.âp1:A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A (T1 â¦) (A href="cic:/matita/basics/logic/R1.def(2)"R1/A T0 a0 T1 a1 x0 p0) x1.
+ âx2:T2 x0 p0 x1 p1.âp2:A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A (T2 â¦) (A href="cic:/matita/basics/logic/R2.def(3)"R2/A T0 a0 T1 a1 T2 a2 x0 p0 x1 p1) x2.
+ âx3:T3 x0 p0 x1 p1 x2 p2.âp3:A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A (T3 â¦) (A href="cic:/matita/basics/logic/R3.def(4)"R3/A T0 a0 T1 a1 T2 a2 T3 a3 x0 p0 x1 p1 x2 p2) x3.
Type[0].
- âa4:T4 a0 (refl T0 a0) a1 (refl (T1 a0 (refl T0 a0)) a1)
- a2 (refl (T2 a0 (refl T0 a0) a1 (refl (T1 a0 (refl T0 a0)) a1)) a2)
- a3 (refl (T3 a0 (refl T0 a0) a1 (refl (T1 a0 (refl T0 a0)) a1)
- a2 (refl (T2 a0 (refl T0 a0) a1 (refl (T1 a0 (refl T0 a0)) a1)) a2))
+ âa4:T4 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A T0 a0) a1 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A (T1 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A T0 a0)) a1)
+ a2 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A (T2 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A T0 a0) a1 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A (T1 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A T0 a0)) a1)) a2)
+ a3 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A (T3 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A T0 a0) a1 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A (T1 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A T0 a0)) a1)
+ a2 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A (T2 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A T0 a0) a1 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A (T1 a0 (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A T0 a0)) a1)) a2))
a3).
âb0:T0.
- âe0:eq (T0 â¦) a0 b0.
+ âe0:A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A (T0 â¦) a0 b0.
âb1: T1 b0 e0.
- âe1:eq (T1 â¦) (R1 T0 a0 T1 a1 b0 e0) b1.
+ âe1:A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A (T1 â¦) (A href="cic:/matita/basics/logic/R1.def(2)"R1/A T0 a0 T1 a1 b0 e0) b1.
âb2: T2 b0 e0 b1 e1.
- âe2:eq (T2 â¦) (R2 T0 a0 T1 a1 T2 a2 b0 e0 b1 e1) b2.
+ âe2:A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A (T2 â¦) (A href="cic:/matita/basics/logic/R2.def(3)"R2/A T0 a0 T1 a1 T2 a2 b0 e0 b1 e1) b2.
âb3: T3 b0 e0 b1 e1 b2 e2.
- âe3:eq (T3 â¦) (R3 T0 a0 T1 a1 T2 a2 T3 a3 b0 e0 b1 e1 b2 e2) b3.
+ âe3:A href="cic:/matita/basics/logic/eq.ind(1,0,2)"eq/A (T3 â¦) (A href="cic:/matita/basics/logic/R3.def(4)"R3/A T0 a0 T1 a1 T2 a2 T3 a3 b0 e0 b1 e1 b2 e2) b3.
T4 b0 e0 b1 e1 b2 e2 b3 e3.
#T0 #a0 #T1 #a1 #T2 #a2 #T3 #a3 #T4 #a4 #b0 #e0 #b1 #e1 #b2 #e2 #b3 #e3
-@(eq_rect_Type0 ????? e3)
-@(R3 ????????? e0 ? e1 ? e2)
+@(A href="cic:/matita/basics/logic/eq_rect_Type0.fix(0,5,1)"eq_rect_Type0/A ????? e3)
+@(A href="cic:/matita/basics/logic/R3.def(4)"R3/A ????????? e0 ? e1 ? e2)
@a4
qed.
(* TODO concrete definition by means of proof irrelevance *)
-axiom streicherK : âT:Type[1].ât:T.âP:t = t â Type[2].P (refl ? t) â âp.P p.
\ No newline at end of file
+axiom streicherK : âT:Type[1].ât:T.âP:t A title="leibnitz's equality" href="cic:/fakeuri.def(1)"=/A t â Type[2].P (A href="cic:/matita/basics/logic/eq.con(0,1,2)"refl/A ? t) â âp.P p.