X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Fsteps%2Frtc_plus.ma;h=6993f318d1c7176c7efef18da714a6562a6476ab;hp=49d25453c3d236dc1914d7e28ecf130cb15b498c;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1 diff --git a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_plus.ma b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_plus.ma index 49d25453c..6993f318d 100644 --- a/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_plus.ma +++ b/matita/matita/contribs/lambdadelta/ground_2/steps/rtc_plus.ma @@ -58,38 +58,38 @@ qed. (* Properties with test for constrained rt-transition counter ***************) -lemma isrt_plus: ∀n1,n2,c1,c2. 𝐑𝐓⦃n1,c1⦄ → 𝐑𝐓⦃n2,c2⦄ → 𝐑𝐓⦃n1+n2,c1+c2⦄. +lemma isrt_plus: ∀n1,n2,c1,c2. 𝐑𝐓❪n1,c1❫ → 𝐑𝐓❪n2,c2❫ → 𝐑𝐓❪n1+n2,c1+c2❫. #n1 #n2 #c1 #c2 * #ri1 #rs1 #H1 * #ri2 #rs2 #H2 destruct /2 width=3 by ex1_2_intro/ qed. -lemma isrt_plus_O1: ∀n,c1,c2. 𝐑𝐓⦃0,c1⦄ → 𝐑𝐓⦃n,c2⦄ → 𝐑𝐓⦃n,c1+c2⦄. +lemma isrt_plus_O1: ∀n,c1,c2. 𝐑𝐓❪0,c1❫ → 𝐑𝐓❪n,c2❫ → 𝐑𝐓❪n,c1+c2❫. /2 width=1 by isrt_plus/ qed. -lemma isrt_plus_O2: ∀n,c1,c2. 𝐑𝐓⦃n,c1⦄ → 𝐑𝐓⦃0,c2⦄ → 𝐑𝐓⦃n,c1+c2⦄. +lemma isrt_plus_O2: ∀n,c1,c2. 𝐑𝐓❪n,c1❫ → 𝐑𝐓❪0,c2❫ → 𝐑𝐓❪n,c1+c2❫. #n #c1 #c2 #H1 #H2 >(plus_n_O n) /2 width=1 by isrt_plus/ qed. -lemma isrt_succ: ∀n,c. 𝐑𝐓⦃n,c⦄ → 𝐑𝐓⦃↑n,c+𝟘𝟙⦄. +lemma isrt_succ: ∀n,c. 𝐑𝐓❪n,c❫ → 𝐑𝐓❪↑n,c+𝟘𝟙❫. /2 width=1 by isrt_plus/ qed. (* Inversion properties with test for constrained rt-transition counter *****) -lemma isrt_inv_plus: ∀n,c1,c2. 𝐑𝐓⦃n,c1 + c2⦄ → - ∃∃n1,n2. 𝐑𝐓⦃n1,c1⦄ & 𝐑𝐓⦃n2,c2⦄ & n1 + n2 = n. +lemma isrt_inv_plus: ∀n,c1,c2. 𝐑𝐓❪n,c1 + c2❫ → + ∃∃n1,n2. 𝐑𝐓❪n1,c1❫ & 𝐑𝐓❪n2,c2❫ & n1 + n2 = n. #n #c1 #c2 * #ri #rs #H elim (plus_inv_dx … H) -H #ri1 #rs1 #ti1 #ts1 #ri2 #rs2 #ti2 #ts2 #_ #_ #H1 #H2 #H3 #H4 elim (plus_inv_O3 … H1) -H1 /3 width=5 by ex3_2_intro, ex1_2_intro/ qed-. -lemma isrt_inv_plus_O_dx: ∀n,c1,c2. 𝐑𝐓⦃n,c1 + c2⦄ → 𝐑𝐓⦃0,c2⦄ → 𝐑𝐓⦃n,c1⦄. +lemma isrt_inv_plus_O_dx: ∀n,c1,c2. 𝐑𝐓❪n,c1 + c2❫ → 𝐑𝐓❪0,c2❫ → 𝐑𝐓❪n,c1❫. #n #c1 #c2 #H #H2 elim (isrt_inv_plus … H) -H #n1 #n2 #Hn1 #Hn2 #H destruct lapply (isrt_inj … Hn2 H2) -c2 #H destruct // qed-. -lemma isrt_inv_plus_SO_dx: ∀n,c1,c2. 𝐑𝐓⦃n,c1 + c2⦄ → 𝐑𝐓⦃1,c2⦄ → - ∃∃m. 𝐑𝐓⦃m,c1⦄ & n = ↑m. +lemma isrt_inv_plus_SO_dx: ∀n,c1,c2. 𝐑𝐓❪n,c1 + c2❫ → 𝐑𝐓❪1,c2❫ → + ∃∃m. 𝐑𝐓❪m,c1❫ & n = ↑m. #n #c1 #c2 #H #H2 elim (isrt_inv_plus … H) -H #n1 #n2 #Hn1 #Hn2 #H destruct lapply (isrt_inj … Hn2 H2) -c2 #H destruct