lemma tw_shift: ∀L,T. #[L, T] ≤ #[L @ T].
#L elim L //
#K #I #V #IHL #T
-@transitive_le [3: @IHL |2: /2/ | skip ]
+@transitive_le [3: @IHL |2: /2 width=1/ | skip ]
qed.
(* Basic_1: removed theorems 6:
(**************************************************************************)
(* THE FORMAL SYSTEM λδ - MATITA SOURCE FILES
- * Specification started: 2011 April 17
* Confluence of context-sensitive parallel reduction closed: 2011 September 21
* Confluence of context-free parallel reduction closed: 2011 September 6
- * - Patience on me so that I gain peace and perfection! -
+ * Specification started: 2011 April 17
+ * - Patience on me to gain peace and perfection! -
* [ suggested invocation to start formal specifications with ]
*)
lsubs d e L1 L2 → lsubs (d + 1) e (L1. 𝕓{I1} V1) (L2. 𝕓{I2} V2)
.
-interpretation "local environment refinement (substitution)" 'SubEq L1 d e L2 = (lsubs d e L1 L2).
+interpretation
+ "local environment refinement (substitution)"
+ 'SubEq L1 d e L2 = (lsubs d e L1 L2).
definition lsubs_conf: ∀S. (lenv → relation S) → Prop ≝ λS,R.
∀L1,s1,s2. R L1 s1 s2 →
(* Basic properties *********************************************************)
lemma TC_lsubs_conf: ∀S,R. lsubs_conf S R → lsubs_conf S (λL. (TC … (R L))).
-#S #R #HR #L1 #s1 #s2 #H elim H -H s2
+#S #R #HR #L1 #s1 #s2 #H elim H -s2
[ /3 width=5/
| #s #s2 #_ #Hs2 #IHs1 #L2 #d #e #HL12
- lapply (HR … Hs2 … HL12) -HR Hs2 HL12 /3/
+ lapply (HR … Hs2 … HL12) -HR -Hs2 -HL12 /3 width=3/
]
qed.
lemma lsubs_bind_eq: ∀L1,L2,e. L1 [0, e] ≼ L2 → ∀I,V.
L1. 𝕓{I} V [0, e + 1] ≼ L2.𝕓{I} V.
-#L1 #L2 #e #HL12 #I #V elim I -I /2/
+#L1 #L2 #e #HL12 #I #V elim I -I /2 width=1/
qed.
lemma lsubs_refl: ∀d,e,L. L [d, e] ≼ L.
#d elim d -d
-[ #e elim e -e // #e #IHe #L elim L -L /2/
-| #d #IHd #e #L elim L -L /2/
+[ #e elim e -e // #e #IHe #L elim L -L // /2 width=1/
+| #d #IHd #e #L elim L -L // /2 width=1/
]
qed.
lemma lsubs_skip_lt: ∀L1,L2,d,e. L1 [d - 1, e] ≼ L2 → 0 < d →
∀I1,I2,V1,V2. L1. 𝕓{I1} V1 [d, e] ≼ L2. 𝕓{I2} V2.
-#L1 #L2 #d #e #HL12 #Hd >(plus_minus_m_m d 1) /2/
+#L1 #L2 #d #e #HL12 #Hd >(plus_minus_m_m d 1) // /2 width=1/
qed.
(* Basic inversion lemmas ***************************************************)
fact lsubs_fwd_length_full1_aux: ∀L1,L2,d,e. L1 [d, e] ≼ L2 →
d = 0 → e = |L1| → |L1| ≤ |L2|.
-#L1 #L2 #d #e #H elim H -H L1 L2 d e; normalize
+#L1 #L2 #d #e #H elim H -L1 -L2 -d -e normalize
[ //
-| /2/
-| /3/
-| /3/
+| /2 width=1/
+| /3 width=1/
+| /3 width=1/
| #L1 #L2 #_ #_ #_ #_ #d #e #_ #_ #H
elim (plus_S_eq_O_false … H)
-]
+]
qed.
lemma lsubs_fwd_length_full1: ∀L1,L2. L1 [0, |L1|] ≼ L2 → |L1| ≤ |L2|.
fact lsubs_fwd_length_full2_aux: ∀L1,L2,d,e. L1 [d, e] ≼ L2 →
d = 0 → e = |L2| → |L2| ≤ |L1|.
-#L1 #L2 #d #e #H elim H -H L1 L2 d e; normalize
+#L1 #L2 #d #e #H elim H -L1 -L2 -d -e normalize
[ //
-| /2/
-| /3/
-| /3/
+| /2 width=1/
+| /3 width=1/
+| /3 width=1/
| #L1 #L2 #_ #_ #_ #_ #d #e #_ #_ #H
elim (plus_S_eq_O_false … H)
-]
+]
qed.
lemma lsubs_fwd_length_full2: ∀L1,L2. L1 [0, |L2|] ≼ L2 → |L2| ≤ |L1|.
#I #T #V elim V -V
[ #J #H destruct
| #J #W #U #IHW #_ #H destruct
-(*
- (generalize in match e1) -e1 >e0 normalize
-*) -I /2/ (**) (* destruct: one quality is not simplified, the destucted equality is not erased *)
+ -H >e0 in e1; normalize (**) (* destruct: one quality is not simplified, the destucted equality is not erased *)
+ /2 width=1/
]
qed-.
lemma discr_tpair_xy_y: ∀I,V,T. 𝕔{I} V. T = T → False.
#I #V #T elim T -T
[ #J #H destruct
-| #J #W #U #_ #IHU #H destruct -I V /2/ (**) (* destruct: the destucted equality is not erased *)
+| #J #W #U #_ #IHU #H destruct
+ -H (**) (* destruct: the destucted equality is not erased *)
+ /2 width=1/
]
qed-.
(* Basic_1: was: tweight_lt *)
lemma tw_pos: ∀T. 1 ≤ #[T].
-#T elim T -T /2/
+#T elim T -T //
qed.
(* Basic eliminators ********************************************************)
(* Basic_1: removed theorems 11:
wadd_le wadd_lt wadd_O weight_le weight_eq weight_add_O
- weight_add_S tlt_trans tlt_head_sx tlt_head_dx tlt_wf_ind
+ weight_add_S tlt_trans tlt_head_sx tlt_head_dx tlt_wf_ind
removed local theorems 1: q_ind
*)
(* Basic properties *********************************************************)
lemma thom_sym: ∀T1,T2. T1 ≈ T2 → T2 ≈ T1.
-#T1 #T2 #H elim H -H T1 T2 /2/
+#T1 #T2 #H elim H -T1 -T2 /2 width=1/
qed.
lemma thom_refl2: ∀T1,T2. T1 ≈ T2 → T2 ≈ T2.
-#T1 #T2 #H elim H -H T1 T2 /2/
+#T1 #T2 #H elim H -T1 -T2 // /2 width=1/
qed.
lemma thom_refl1: ∀T1,T2. T1 ≈ T2 → T1 ≈ T1.
-/3/ qed.
+/3 width=2/ qed.
lemma simple_thom_repl_dx: ∀T1,T2. T1 ≈ T2 → 𝕊[T1] → 𝕊[T2].
-#T1 #T2 #H elim H -H T1 T2 //
+#T1 #T2 #H elim H -T1 -T2 //
#V1 #V2 #T1 #T2 #H
elim (simple_inv_bind … H)
qed. (**) (* remove from index *)
lemma simple_thom_repl_sn: ∀T1,T2. T1 ≈ T2 → 𝕊[T2] → 𝕊[T1].
-/3/ qed-.
+/3 width=3/ qed-.
(* Basic inversion lemmas ***************************************************)
fact thom_inv_bind1_aux: ∀T1,T2. T1 ≈ T2 → ∀I,W1,U1. T1 = 𝕓{I}W1.U1 →
∃∃W2,U2. I = Abst & T2 = 𝕔{Abst} W2. U2.
-#T1 #T2 * -T1 T2
+#T1 #T2 * -T1 -T2
[ #J #I #W1 #U1 #H destruct
-| #V1 #V2 #T1 #T2 #I #W1 #U1 #H destruct -V1 T1 /2/
+| #V1 #V2 #T1 #T2 #I #W1 #U1 #H destruct /2 width=3/
| #V1 #V2 #T1 #T2 #H_ #_ #_ #I #W1 #U1 #H destruct
]
qed.
fact thom_inv_flat1_aux: ∀T1,T2. T1 ≈ T2 → ∀I,W1,U1. T1 = 𝕗{I}W1.U1 →
∃∃W2,U2. U1 ≈ U2 & 𝕊[U1] & 𝕊[U2] &
I = Appl & T2 = 𝕔{Appl} W2. U2.
-#T1 #T2 * -T1 T2
+#T1 #T2 * -T1 -T2
[ #J #I #W1 #U1 #H destruct
| #V1 #V2 #T1 #T2 #I #W1 #U1 #H destruct
-| #V1 #V2 #T1 #T2 #HT12 #HT1 #HT2 #I #W1 #U1 #H destruct -V1 T1 /2 width=5/
+| #V1 #V2 #T1 #T2 #HT12 #HT1 #HT2 #I #W1 #U1 #H destruct /2 width=5/
]
qed.
lemma thom_inv_flat1: ∀I,W1,U1,T2. 𝕗{I}W1.U1 ≈ T2 →
∃∃W2,U2. U1 ≈ U2 & 𝕊[U1] & 𝕊[U2] &
I = Appl & T2 = 𝕔{Appl} W2. U2.
-/2/ qed-.
+/2 width=4/ qed-.
(* Basic_1: removed theorems 7:
iso_gen_sort iso_gen_lref iso_gen_head iso_refl iso_trans
non associative with precedence 45
for @{ 'PSubstStar $L $T1 $d $e $T2 }.
+notation "hvbox( T1 break [ d , break e ] ≡ break T2 )"
+ non associative with precedence 45
+ for @{ 'TSubst $T1 $d $e $T2 }.
+
notation "hvbox( L ⊢ break term 90 T1 break [ d , break e ] ≡ break T2 )"
non associative with precedence 45
for @{ 'TSubst $L $T1 $d $e $T2 }.
#!/bin/sh
for MA in `find -name "*.ma"`; do
- echo ${MA}; sed "s/$1/$2/g" ${MA} > ${MA}.new
+ echo ${MA}; sed "s!$1!$2!g" ${MA} > ${MA}.new
if diff ${MA} ${MA}.new > /dev/null;
- then rm -f ${MA}.new; else mv -f ${MA}.new ${MA}; fi
+ then rm -f ${MA}.new;
+ else mv -f ${MA} ${MA}.old; mv -f ${MA}.new ${MA};
+ fi
done
unset MA