X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Fsteps%2Frtc_ist_max.ma;h=6c161f653afe4342892e3740d1313969f2558135;hp=ba31b7faaefc5301a461a195745e4f621cef51d5;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1 diff --git a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_max.ma b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_max.ma index ba31b7faa..6c161f653 100644 --- a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_max.ma +++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_max.ma @@ -19,26 +19,26 @@ include "ground_2/steps/rtc_ist.ma". (* Properties with test for t-transition counter ****************************) -lemma ist_max: ∀n1,n2,c1,c2. 𝐓⦃n1,c1⦄ → 𝐓⦃n2,c2⦄ → 𝐓⦃n1∨n2,c1∨c2⦄. +lemma ist_max: ∀n1,n2,c1,c2. 𝐓❪n1,c1❫ → 𝐓❪n2,c2❫ → 𝐓❪n1∨n2,c1∨c2❫. #n1 #n2 #c1 #c2 #H1 #H2 destruct // qed. -lemma ist_max_O1: ∀n,c1,c2. 𝐓⦃0,c1⦄ → 𝐓⦃n,c2⦄ → 𝐓⦃n,c1∨c2⦄. +lemma ist_max_O1: ∀n,c1,c2. 𝐓❪0,c1❫ → 𝐓❪n,c2❫ → 𝐓❪n,c1∨c2❫. /2 width=1 by ist_max/ qed. -lemma ist_max_O2: ∀n,c1,c2. 𝐓⦃n,c1⦄ → 𝐓⦃0,c2⦄ → 𝐓⦃n,c1∨c2⦄. +lemma ist_max_O2: ∀n,c1,c2. 𝐓❪n,c1❫ → 𝐓❪0,c2❫ → 𝐓❪n,c1∨c2❫. #n #c1 #c2 #H1 #H2 >(max_O2 n) /2 width=1 by ist_max/ qed. -lemma ist_max_idem1: ∀n,c1,c2. 𝐓⦃n,c1⦄ → 𝐓⦃n,c2⦄ → 𝐓⦃n,c1∨c2⦄. +lemma ist_max_idem1: ∀n,c1,c2. 𝐓❪n,c1❫ → 𝐓❪n,c2❫ → 𝐓❪n,c1∨c2❫. #n #c1 #c2 #H1 #H2 >(idempotent_max n) /2 width=1 by ist_max/ qed. (* Inversion properties with test for t-transition counter ******************) lemma ist_inv_max: - ∀n,c1,c2. 𝐓⦃n,c1 ∨ c2⦄ → - ∃∃n1,n2. 𝐓⦃n1,c1⦄ & 𝐓⦃n2,c2⦄ & (n1 ∨ n2) = n. + ∀n,c1,c2. 𝐓❪n,c1 ∨ c2❫ → + ∃∃n1,n2. 𝐓❪n1,c1❫ & 𝐓❪n2,c2❫ & (n1 ∨ n2) = n. #n #c1 #c2 #H elim (max_inv_dx … H) -H #ri1 #rs1 #ti1 #ts1 #ri2 #rs2 #ti2 #ts2 #H1 #H2 #H3 #H4 #H5 #H6 destruct elim (max_inv_O3 … H1) -H1 #H11 #H12 destruct @@ -47,14 +47,14 @@ elim (max_inv_O3 … H3) -H3 #H31 #H32 destruct /2 width=5 by ex3_2_intro/ qed-. -lemma ist_O_inv_max: ∀c1,c2. 𝐓⦃0,c1 ∨ c2⦄ → ∧∧ 𝐓⦃0,c1⦄ & 𝐓⦃0,c2⦄. +lemma ist_O_inv_max: ∀c1,c2. 𝐓❪0,c1 ∨ c2❫ → ∧∧ 𝐓❪0,c1❫ & 𝐓❪0,c2❫. #c1 #c2 #H elim (ist_inv_max … H) -H #n1 #n2 #Hn1 #Hn2 #H elim (max_inv_O3 … H) -H #H1 #H2 destruct /2 width=1 by conj/ qed-. -lemma ist_inv_max_O_dx: ∀n,c1,c2. 𝐓⦃n,c1 ∨ c2⦄ → 𝐓⦃0,c2⦄ → 𝐓⦃n,c1⦄. +lemma ist_inv_max_O_dx: ∀n,c1,c2. 𝐓❪n,c1 ∨ c2❫ → 𝐓❪0,c2❫ → 𝐓❪n,c1❫. #n #c1 #c2 #H #H2 elim (ist_inv_max … H) -H #n1 #n2 #Hn1 #Hn2 #H destruct // qed-.