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_plus.ma;h=7e154d6b973e6c6113beb58cc65c28ab6796d1f8;hp=a66a81d29ac882bfb0c8cff1dbb1f3ccee47a1ac;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1 diff --git a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_plus.ma b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_plus.ma index a66a81d29..7e154d6b9 100644 --- a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_plus.ma +++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_ist_plus.ma @@ -19,25 +19,25 @@ include "ground_2/steps/rtc_ist.ma". (* Properties with test for t-transition counter ****************************) -lemma ist_plus: ∀n1,n2,c1,c2. 𝐓⦃n1,c1⦄ → 𝐓⦃n2,c2⦄ → 𝐓⦃n1+n2,c1+c2⦄. +lemma ist_plus: ∀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_plus_O1: ∀n,c1,c2. 𝐓⦃0,c1⦄ → 𝐓⦃n,c2⦄ → 𝐓⦃n,c1+c2⦄. +lemma ist_plus_O1: ∀n,c1,c2. 𝐓❪0,c1❫ → 𝐓❪n,c2❫ → 𝐓❪n,c1+c2❫. /2 width=1 by ist_plus/ qed. -lemma ist_plus_O2: ∀n,c1,c2. 𝐓⦃n,c1⦄ → 𝐓⦃0,c2⦄ → 𝐓⦃n,c1+c2⦄. +lemma ist_plus_O2: ∀n,c1,c2. 𝐓❪n,c1❫ → 𝐓❪0,c2❫ → 𝐓❪n,c1+c2❫. #n #c1 #c2 #H1 #H2 >(plus_n_O n) /2 width=1 by ist_plus/ qed. -lemma ist_succ: ∀n,c. 𝐓⦃n,c⦄ → 𝐓⦃↑n,c+𝟘𝟙⦄. +lemma ist_succ: ∀n,c. 𝐓❪n,c❫ → 𝐓❪↑n,c+𝟘𝟙❫. /2 width=1 by ist_plus/ qed. (* Inversion properties with test for constrained rt-transition counter *****) lemma ist_inv_plus: - ∀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 (plus_inv_dx … H) -H #ri1 #rs1 #ti1 #ts1 #ri2 #rs2 #ti2 #ts2 #H1 #H2 #H3 #H4 #H5 #H6 destruct elim (plus_inv_O3 … H1) -H1 #H11 #H12 destruct @@ -46,20 +46,20 @@ elim (plus_inv_O3 … H3) -H3 #H31 #H32 destruct /3 width=5 by ex3_2_intro/ qed-. -lemma ist_inv_plus_O_dx: ∀n,c1,c2. 𝐓⦃n,c1 + c2⦄ → 𝐓⦃0,c2⦄ → 𝐓⦃n,c1⦄. +lemma ist_inv_plus_O_dx: ∀n,c1,c2. 𝐓❪n,c1 + c2❫ → 𝐓❪0,c2❫ → 𝐓❪n,c1❫. #n #c1 #c2 #H #H2 elim (ist_inv_plus … H) -H #n1 #n2 #Hn1 #Hn2 #H destruct // qed-. lemma ist_inv_plus_SO_dx: - ∀n,c1,c2. 𝐓⦃n,c1 + c2⦄ → 𝐓⦃1,c2⦄ → - ∃∃m. 𝐓⦃m,c1⦄ & n = ↑m. + ∀n,c1,c2. 𝐓❪n,c1 + c2❫ → 𝐓❪1,c2❫ → + ∃∃m. 𝐓❪m,c1❫ & n = ↑m. #n #c1 #c2 #H #H2 destruct elim (ist_inv_plus … H) -H #n1 #n2 #Hn1 #Hn2 #H destruct /2 width=3 by ex2_intro/ qed-. -lemma ist_inv_plus_10_dx: ∀n,c. 𝐓⦃n,c+𝟙𝟘⦄ → ⊥. +lemma ist_inv_plus_10_dx: ∀n,c. 𝐓❪n,c+𝟙𝟘❫ → ⊥. #n #c #H elim (ist_inv_plus … H) -H #n1 #n2 #_ #H #_ /2 width=2 by ist_inv_10/