- partial commit of rt_transition ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / examples / ex_fpbg_refl.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/examples/ex_fpbg_refl.ma b/matita/matita/contribs/lambdadelta/basic_2/examples/ex_fpbg_refl.ma
index fbc2bd7cd1a117058e4a9f1a37245314371d468c..e37f8831f0689d63dfb49c72c875ad3da8ab7fd0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/examples/ex_fpbg_refl.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/examples/ex_fpbg_refl.ma
@@ -18,37 +18,37 @@ include "basic_2/computation/fpbg_fpbs.ma".
 
 (* Reflexivity of proper qrst-computation: the term ApplOmega ***************)
 
-definition ApplDelta: term → nat → term ≝ λW,k. +ⓛW.ⓐ⋆k.ⓐ#0.#0.
+definition ApplDelta: term → nat → term ≝ λW,s. +ⓛW.ⓐ⋆s.ⓐ#0.#0.
 
-definition ApplOmega1: term → nat → term ≝ λW,k. ⓐ(ApplDelta W k).(ApplDelta W k).
+definition ApplOmega1: term → nat → term ≝ λW,s. ⓐ(ApplDelta W s).(ApplDelta W s).
 
-definition ApplOmega2: term → nat → term ≝ λW,k. +ⓓⓝW.(ApplDelta W k).ⓐ⋆k.ⓐ#0.#0.
+definition ApplOmega2: term → nat → term ≝ λW,s. +ⓓⓝW.(ApplDelta W s).ⓐ⋆s.ⓐ#0.#0.
 
-definition ApplOmega3: term → nat → term ≝ λW,k. ⓐ⋆k.(ApplOmega1 W k).
+definition ApplOmega3: term → nat → term ≝ λW,s. ⓐ⋆s.(ApplOmega1 W s).
 
 (* Basic properties *********************************************************)
 
-lemma ApplDelta_lift: ∀W1,W2,k,l,m. ⬆[l, m] W1 ≡ W2 →
-                      ⬆[l, m] (ApplDelta W1 k) ≡ (ApplDelta W2 k).
+lemma ApplDelta_lift: ∀W1,W2,s,l,k. ⬆[l, k] W1 ≡ W2 →
+                      ⬆[l, k] (ApplDelta W1 s) ≡ (ApplDelta W2 s).
 /5 width=1 by lift_flat, lift_bind, lift_lref_lt/ qed.
 
-lemma cpr_ApplOmega_12: ∀G,L,W,k. ⦃G, L⦄ ⊢ ApplOmega1 W k ➡ ApplOmega2 W k.
+lemma cpr_ApplOmega_12: ∀G,L,W,s. ⦃G, L⦄ ⊢ ApplOmega1 W s ➡ ApplOmega2 W s.
 /2 width=1 by cpr_beta/ qed.
 
-lemma cpr_ApplOmega_23: ∀G,L,W,k. ⦃G, L⦄ ⊢ ApplOmega2 W k ➡ ApplOmega3 W k.
-#G #L #W1 #k elim (lift_total W1 0 1) #W2 #HW12
-@(cpr_zeta … (ApplOmega3 W2 k)) /4 width=1 by ApplDelta_lift, lift_flat/
-@cpr_flat // @cpr_flat @(cpr_delta … (ApplDelta W1 k) ? 0)
+lemma cpr_ApplOmega_23: ∀G,L,W,s. ⦃G, L⦄ ⊢ ApplOmega2 W s ➡ ApplOmega3 W s.
+#G #L #W1 #s elim (lift_total W1 0 1) #W2 #HW12
+@(cpr_zeta … (ApplOmega3 W2 s)) /4 width=1 by ApplDelta_lift, lift_flat/
+@cpr_flat // @cpr_flat @(cpr_delta … (ApplDelta W1 s) ? 0)
 [3,5,8,10: /2 width=2 by ApplDelta_lift/ |4,9: /2 width=1 by cpr_eps/ |*: skip ]
 qed.
 
-lemma cpxs_ApplOmega_13: ∀h,g,G,L,W,k. ⦃G, L⦄ ⊢ ApplOmega1 W k ➡*[h,g] ApplOmega3 W k.
+lemma cpxs_ApplOmega_13: ∀h,o,G,L,W,s. ⦃G, L⦄ ⊢ ApplOmega1 W s ➡*[h,o] ApplOmega3 W s.
 /4 width=3 by cpxs_strap1, cpr_cpx/ qed.
 
-lemma fqup_ApplOmega_13: ∀G,L,W,k. ⦃G, L, ApplOmega3 W k⦄ ⊐+ ⦃G, L, ApplOmega1 W k⦄.
+lemma fqup_ApplOmega_13: ∀G,L,W,s. ⦃G, L, ApplOmega3 W s⦄ ⊐+ ⦃G, L, ApplOmega1 W s⦄.
 /2 width=1 by/ qed.
 
 (* Main properties **********************************************************)
 
-theorem fpbg_refl: ∀h,g,G,L,W,k. ⦃G, L, ApplOmega1 W k⦄ >≡[h,g] ⦃G, L, ApplOmega1 W k⦄.
+theorem fpbg_refl: ∀h,o,G,L,W,s. ⦃G, L, ApplOmega1 W s⦄ >≡[h,o] ⦃G, L, ApplOmega1 W s⦄.
 /3 width=5 by fpbs_fpbg_trans, fqup_fpbg, cpxs_fpbs/ qed.