From e63beeff229680e6f6933fc7095e0910dbb56209 Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Thu, 1 Mar 2007 15:45:33 +0000 Subject: [PATCH] procedural proof of ty3_gen_cast --- helm/software/matita/contribs/prova.ma | 232 ++++++++++++++++++------- 1 file changed, 172 insertions(+), 60 deletions(-) diff --git a/helm/software/matita/contribs/prova.ma b/helm/software/matita/contribs/prova.ma index cab82e7df..b975eaffb 100644 --- a/helm/software/matita/contribs/prova.ma +++ b/helm/software/matita/contribs/prova.ma @@ -15,66 +15,178 @@ set "baseuri" "cic:/matita/test/prova". include "LAMBDA-TYPES/LambdaDelta-1/preamble.ma". - -alias id "Abst" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/T/defs/B.ind#xpointer(1/1/2)". -alias id "Abbr" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/T/defs/B.ind#xpointer(1/1/1)". -(* -alias id "B" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/T/defs/B.ind#xpointer(1/1)". -*) -theorem not_abbr_abst: - (Abbr\neq Abst) -.(* tactics: 7 *) -whd in \vdash (%). -intros 1 (H). -letin DEFINED \def (\lambda ee:B - .match ee in B return \lambda _:B.Prop with - [Abbr\rArr True|Abst\rArr False|Void\rArr False]).(* extracted *) -cut (DEFINED Abbr) as ASSUMED; -[rewrite > H in ASSUMED:(%) as (H0) -|apply I +alias id "ty3" = "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/ty3/defs/ty3.ind#xpointer(1/1)". +alias id "pc3" = "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/pc3/defs/pc3.con". +alias id "THead" = "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/T/defs/T.ind#xpointer(1/1/3)". +alias id "T" = "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/T/defs/T.ind#xpointer(1/1)". +alias id "G" = "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/G/defs/G.ind#xpointer(1/1)". +alias id "Flat" = "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/T/defs/K.ind#xpointer(1/1/2)". +alias id "Cast" = "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/T/defs/F.ind#xpointer(1/1/2)". +alias id "C" = "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/C/defs/C.ind#xpointer(1/1)". +theorem ty3_gen_cast: + (\forall g:G + .\forall c:C + .\forall t1:T + .\forall t2:T + .\forall x:T + .ty3 g c (THead (Flat Cast) t2 t1) x + \rarr pc3 c t2 x\land ty3 g c t1 t2) +. +(* tactics: 68 *) +intros 6 (g c t1 t2 x H). +apply insert_eq;(* 6 P P P C I I 3 0 *) +[apply T(* dependent *) +|apply (THead (Flat Cast) t2 t1)(* dependent *) +|apply (\lambda t:T.ty3 g c t x)(* dependent *) +|intros 2 (y H0). +alias id "ty3_ind" = "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/ty3/defs/ty3_ind.con". +elim H0 using ty3_ind names 0;(* 13 P C I I I I I I I C C C I 12 3 *) +[intros 11 (c0 t0 t UNUSED UNUSED u t3 UNUSED H4 H5 H6). +letin H7 \def (f_equal T T (\lambda e:T.e) u (THead (Flat Cast) t2 t1) H6).(* 6 C C C C C I *) +clearbody H7. +rewrite > H7 in H4:(%) as (H8). +cut (pc3 c0 t2 t3\land ty3 g c0 t1 t2) as H10; +[id +|apply H8.(* 1 I *) +apply refl_equal(* 2 C C *) +]. +elim H10 using and_ind names 0.(* 5 P P C I I 3 0 *) +intros 2 (H11 H12). +apply conj;(* 4 C C I I *) +[alias id "pc3_t" = "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/pc3/props/pc3_t.con". +apply pc3_t;(* 6 P C C I C I *) +[apply t3(* dependent *) +|apply H11(* assumption *) +|apply H5(* assumption *) +] +|apply H12(* assumption *) +] +|intros 3 (c0 m H1). +alias id "K" = "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/T/defs/K.ind#xpointer(1/1)". +cut match THead (Flat Cast) t2 t1 in T return \lambda _:T.Prop with +[TSort (_:nat)\rArr True +|TLRef (_:nat)\rArr False +|THead (_:K) (_:T) (_:T)\rArr False] as H2; +[id +|rewrite < H1 in \vdash (%). +apply I +]. +clearbody H2. +change in H2:(%) with match THead (Flat Cast) t2 t1 in T return \lambda _:T.Prop with +[TSort (_:nat)\rArr True +|TLRef (_:nat)\rArr False +|THead (_:K) (_:T) (_:T)\rArr False]. +elim H2 using False_ind names 0(* 2 C I 2 0 *) +|intros 9 (n c0 d u UNUSED t UNUSED UNUSED H4). +cut match THead (Flat Cast) t2 t1 in T return \lambda _:T.Prop with +[TSort (_:nat)\rArr False +|TLRef (_:nat)\rArr True +|THead (_:K) (_:T) (_:T)\rArr False] as H5; +[id +|rewrite < H4 in \vdash (%). +apply I +]. +clearbody H5. +change in H5:(%) with match THead (Flat Cast) t2 t1 in T return \lambda _:T.Prop with +[TSort (_:nat)\rArr False +|TLRef (_:nat)\rArr True +|THead (_:K) (_:T) (_:T)\rArr False]. +elim H5 using False_ind names 0(* 2 C I 2 0 *) +|intros 9 (n c0 d u UNUSED t UNUSED UNUSED H4). +cut match THead (Flat Cast) t2 t1 in T return \lambda _:T.Prop with +[TSort (_:nat)\rArr False +|TLRef (_:nat)\rArr True +|THead (_:K) (_:T) (_:T)\rArr False] as H5; +[id +|rewrite < H4 in \vdash (%). +apply I +]. +clearbody H5. +change in H5:(%) with match THead (Flat Cast) t2 t1 in T return \lambda _:T.Prop with +[TSort (_:nat)\rArr False +|TLRef (_:nat)\rArr True +|THead (_:K) (_:T) (_:T)\rArr False]. +elim H5 using False_ind names 0(* 2 C I 2 0 *) +|intros 14 (c0 u t UNUSED UNUSED b t0 t3 UNUSED UNUSED t4 UNUSED UNUSED H7). +alias id "F" = "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/T/defs/F.ind#xpointer(1/1)". +alias id "B" = "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/T/defs/B.ind#xpointer(1/1)". +cut match THead (Flat Cast) t2 t1 in T return \lambda _:T.Prop with +[TSort (_:nat)\rArr False +|TLRef (_:nat)\rArr False +|THead (k:K) (_:T) (_:T)\rArr + match k in K return \lambda _:K.Prop with + [Bind (_:B)\rArr True|Flat (_:F)\rArr False]] as H8; +[id +|rewrite < H7 in \vdash (%). +apply I +]. +clearbody H8. +change in H8:(%) with match THead (Flat Cast) t2 t1 in T return \lambda _:T.Prop with +[TSort (_:nat)\rArr False +|TLRef (_:nat)\rArr False +|THead (k:K) (_:T) (_:T)\rArr + match k in K return \lambda _:K.Prop with + [Bind (_:B)\rArr True|Flat (_:F)\rArr False]]. +elim H8 using False_ind names 0(* 2 C I 2 0 *) +|intros 10 (c0 w u UNUSED UNUSED v t UNUSED UNUSED H5). +cut match THead (Flat Cast) t2 t1 in T return \lambda _:T.Prop with +[TSort (_:nat)\rArr False +|TLRef (_:nat)\rArr False +|THead (k:K) (_:T) (_:T)\rArr + match k in K return \lambda _:K.Prop with + [Bind (_:B)\rArr False + |Flat (f:F)\rArr + match f in F return \lambda _:F.Prop with + [Appl\rArr True|Cast\rArr False]]] as H6; +[id +|rewrite < H5 in \vdash (%). +apply I +]. +clearbody H6. +change in H6:(%) with match THead (Flat Cast) t2 t1 in T return \lambda _:T.Prop with +[TSort (_:nat)\rArr False +|TLRef (_:nat)\rArr False +|THead (k:K) (_:T) (_:T)\rArr + match k in K return \lambda _:K.Prop with + [Bind (_:B)\rArr False + |Flat (f:F)\rArr + match f in F return \lambda _:F.Prop with + [Appl\rArr True|Cast\rArr False]]]. +elim H6 using False_ind names 0(* 2 C I 2 0 *) +|intros 9 (c0 t0 t3 H1 H2 t4 UNUSED UNUSED H5). +letin H6 \def (f_equal T T + (\lambda e:T + .match e in T return \lambda _:T.T with + [TSort (_:nat)\rArr t3 + |TLRef (_:nat)\rArr t3 + |THead (_:K) (t:T) (_:T)\rArr t]) (THead (Flat Cast) t3 t0) + (THead (Flat Cast) t2 t1) H5).(* 6 C C C C C I *) +alias id "pc3_refl" = "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/pc3/props/pc3_refl.con". +letin DEFINED \def (let H7 \def + f_equal T T + (\lambda e:T + .match e in T return \lambda _:T.T with + [TSort (_:nat)\rArr t0 + |TLRef (_:nat)\rArr t0 + |THead (_:K) (_:T) (t:T)\rArr t]) + (THead (Flat Cast) t3 t0) (THead (Flat Cast) t2 t1) H5 + in + \lambda H8:t3=t2 + .(let H11 \def + eq_ind T t3 + (\lambda t:T + .t0=THead (Flat Cast) t2 t1 + \rarr pc3 c0 t2 t\land ty3 g c0 t1 t2) H2 t2 H8 + in + let H12 \def eq_ind T t3 (\lambda t:T.ty3 g c0 t0 t) H1 t2 H8 in + eq_ind_r T t2 (\lambda t:T.pc3 c0 t2 t\land ty3 g c0 t1 t2) + (let H14 \def eq_ind T t0 (\lambda t:T.ty3 g c0 t t2) H12 t1 H7 in + conj (pc3 c0 t2 t2) (ty3 g c0 t1 t2) (pc3_refl c0 t2) H14) t3 + H8)). +apply DEFINED.(* 1 I *) +apply H6(* assumption *) +] +|apply H(* assumption *) ]. -elim H0 using False_ind names 0.(* 2 C I 2 0 *) qed. -alias id "Abbr" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/T/defs/B.ind#xpointer(1/1/1)". -alias id "Abst" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/T/defs/B.ind#xpointer(1/1/2)". -alias id "Appl" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/T/defs/F.ind#xpointer(1/1/1)". -alias id "Bind" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/T/defs/K.ind#xpointer(1/1/1)". -alias id "Cast" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/T/defs/F.ind#xpointer(1/1/2)". -alias id "ex2_sym" = "cic:/matita/LAMBDA-TYPES/Level-1/Base/types/props/ex2_sym.con". -alias id "ex3_2_ind" = "cic:/matita/LAMBDA-TYPES/Level-1/Base/types/defs/ex3_2_ind.con". -alias id "Flat" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/T/defs/K.ind#xpointer(1/1/2)". -alias id "lift" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/lift/defs/lift.con". -alias id "or3_ind" = "cic:/matita/LAMBDA-TYPES/Level-1/Base/types/defs/or3_ind.con". -alias id "pr0_beta" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/pr0/defs/pr0.ind#xpointer(1/1/3)". -alias id "pr0" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/pr0/defs/pr0.ind#xpointer(1/1)". -alias id "pr0_comp" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/pr0/defs/pr0.ind#xpointer(1/1/2)". -alias id "pr0_delta" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/pr0/defs/pr0.ind#xpointer(1/1/5)". -alias id "pr0_epsilon" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/pr0/defs/pr0.ind#xpointer(1/1/7)". -alias id "pr0_ind" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/pr0/defs/pr0_ind.con". -alias id "pr0_subst0_fwd" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/pr0/props/pr0_subst0_fwd.con". -alias id "pr0_upsilon" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/pr0/defs/pr0.ind#xpointer(1/1/4)". -alias id "pr0_zeta" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/pr0/defs/pr0.ind#xpointer(1/1/6)". -alias id "s" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/s/defs/s.con". -alias id "subst0_both" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/subst0/defs/subst0.ind#xpointer(1/1/4)". -alias id "subst0" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/subst0/defs/subst0.ind#xpointer(1/1)". -alias id "subst0_confluence_neq" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/subst0/subst0/subst0_confluence_neq.con". -alias id "subst0_fst" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/subst0/defs/subst0.ind#xpointer(1/1/2)". -alias id "subst0_gen_head" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/subst0/fwd/subst0_gen_head.con". -alias id "subst0_gen_lift_ge" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/subst0/fwd/subst0_gen_lift_ge.con". -alias id "subst0_lift_ge_s" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/subst0/props/subst0_lift_ge_s.con". -alias id "subst0_snd" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/subst0/defs/subst0.ind#xpointer(1/1/3)". -alias id "subst0_subst0_back" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/subst0/subst0/subst0_subst0_back.con". -alias id "subst0_trans" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/subst0/subst0/subst0_trans.con". -alias id "T" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/T/defs/T.ind#xpointer(1/1)". -alias id "THead" = "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/T/defs/T.ind#xpointer(1/1/3)". - -inline procedural - "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/pr0/props/pr0_subst0.con". -(* -inline procedural - "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/ty3/pr3/ty3_sred_wcpr0_pr0.con". - -inline procedural - "cic:/Coq/Reals/RiemannInt/FTC_Riemann.con". -*) -- 2.39.2