+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-set "baseuri" "cic:/matita/test/prova".
-
-include "../legacy/coq.ma".
-
-theorem pippo: \forall (A,B:Prop). A \land B \to A.
- intros; decompose; assumption.
-qed.
-
-inline procedural "cic:/matita/test/prova/pippo.con".
-
-alias id "plus" = "cic:/Coq/Init/Peano/plus.con".
-alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
-alias id "eq" = "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1)".
-theorem plus_comm: \forall n:nat.\forall m:nat.eq nat (plus n m) (plus m n).
- intros; alias id "plus_comm" = "cic:/Coq/Arith/Plus/plus_comm.con".
-apply plus_comm.
-qed.
-(*
-include "LAMBDA-TYPES/LambdaDelta-1/preamble.ma".
-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: 80 *)
-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 *)
-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 *)
-letin 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).(* 6 C C C C C I *)
-cut (t3=t2\rarr pc3 c0 t2 t3\land ty3 g c0 t1 t2) as DEFINED;
-[id
-|intros 1 (H8).
-rewrite > H8 in H2:(%) as (UNUSED).
-rewrite > H8 in H1:(%) as (H12).
-rewrite > H8 in \vdash (%).
-clearbody H7.
-change in H7:(%) with (match THead (Flat Cast) t3 t0 in T return \lambda _:T.T with
- [TSort (_:nat)\rArr t0
- |TLRef (_:nat)\rArr t0
- |THead (_:K) (_:T) (t:T)\rArr t]
- =match THead (Flat Cast) t2 t1 in T return \lambda _:T.T with
- [TSort (_:nat)\rArr t0
- |TLRef (_:nat)\rArr t0
- |THead (_:K) (_:T) (t:T)\rArr t]).
-rewrite > H7 in H12:(%) as (H14).
-apply conj;(* 4 C C I I *)
-[alias id "pc3_refl" = "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/pc3/props/pc3_refl.con".
-apply pc3_refl(* 2 C C *)
-|apply H14(* assumption *)
-]
-].
-apply DEFINED.(* 1 I *)
-apply H6(* assumption *)
-]
-|apply H(* assumption *)
-].
-qed.
-*)
-(*
-include "nat/orders.ma".
-
-theorem le_inv:
- \forall P:nat \to Prop
- .\forall p2
- .\forall p1
- .p2 <= p1 \to
- (p1 = p2 \to P p2) \to
- (\forall n1
- .p2 <= n1 \to
- (p1 = n1 \to P n1) \to
- p1 = S n1 \to P (S n1)) \to
- P p1.
- intros 4; elim H names 0; clear H p1; intros;
- [ apply H; reflexivity
- | apply H3; clear H3; intros;
- [ apply H | apply H1; clear H1; intros; subst;
- [ apply H2; apply H3 | ]
- | reflexivity
- ]
-*)
projects / helm.git / blobdiff