X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Fcounters%2Frtc_ist_plus.ma;h=ce43fe2dc50c2e619b017c050042e9f3a5ee57e5;hb=2e4a7c54ef77c10cb1cef4b59518c473245ea935;hp=5156acb85e3c34bcc2a6d39b780fc3ba2e31cc17;hpb=0bcf2dc1a27e38cb6cd3d44eb838d652926841e0;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/ground/counters/rtc_ist_plus.ma b/matita/matita/contribs/lambdadelta/ground/counters/rtc_ist_plus.ma index 5156acb85..ce43fe2dc 100644 --- a/matita/matita/contribs/lambdadelta/ground/counters/rtc_ist_plus.ma +++ b/matita/matita/contribs/lambdadelta/ground/counters/rtc_ist_plus.ma @@ -20,27 +20,27 @@ include "ground/counters/rtc_ist.ma". (* Constructions with rtc_plus **********************************************) -lemma rtc_ist_plus (n1) (n2) (c1) (c2): 𝐓❪n1,c1❫ → 𝐓❪n2,c2❫ → 𝐓❪n1+n2,c1+c2❫. +lemma rtc_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 rtc_ist_plus_zero_sn (n) (c1) (c2): 𝐓❪𝟎,c1❫ → 𝐓❪n,c2❫ → 𝐓❪n,c1+c2❫. +lemma rtc_ist_plus_zero_sn (n) (c1) (c2): 𝐓❨𝟎,c1❩ → 𝐓❨n,c2❩ → 𝐓❨n,c1+c2❩. #n #c1 #c2 #H1 #H2 >(nplus_zero_sn n) /2 width=1 by rtc_ist_plus/ qed. -lemma rtc_ist_plus_zero_dx (n) (c1) (c2): 𝐓❪n,c1❫ → 𝐓❪𝟎,c2❫ → 𝐓❪n,c1+c2❫. +lemma rtc_ist_plus_zero_dx (n) (c1) (c2): 𝐓❨n,c1❩ → 𝐓❨𝟎,c2❩ → 𝐓❨n,c1+c2❩. /2 width=1 by rtc_ist_plus/ qed. -lemma rtc_ist_succ (n) (c): 𝐓❪n,c❫ → 𝐓❪↑n,c+𝟘𝟙❫. +lemma rtc_ist_succ (n) (c): 𝐓❨n,c❩ → 𝐓❨↑n,c+𝟘𝟙❩. #n #c #H >nplus_unit_dx /2 width=1 by rtc_ist_plus/ qed. (* Inversions with rtc_plus *************************************************) -lemma rtc_ist_inv_plus (n) (c1) (c2): 𝐓❪n,c1 + c2❫ → - ∃∃n1,n2. 𝐓❪n1,c1❫ & 𝐓❪n2,c2❫ & n1 + n2 = n. +lemma rtc_ist_inv_plus (n) (c1) (c2): 𝐓❨n,c1 + c2❩ → + ∃∃n1,n2. 𝐓❨n1,c1❩ & 𝐓❨n2,c2❩ & n1 + n2 = n. #n #c1 #c2 #H elim (rtc_plus_inv_dx … H) -H #ri1 #rs1 #ti1 #ts1 #ri2 #rs2 #ti2 #ts2 #H1 #H2 #H3 #H4 #H5 #H6 destruct elim (eq_inv_nplus_zero … H1) -H1 #H11 #H12 destruct @@ -49,20 +49,20 @@ elim (eq_inv_nplus_zero … H3) -H3 #H31 #H32 destruct /3 width=5 by ex3_2_intro/ qed-. -lemma rtc_ist_inv_plus_zero_dx (n) (c1) (c2): 𝐓❪n,c1 + c2❫ → 𝐓❪𝟎,c2❫ → 𝐓❪n,c1❫. +lemma rtc_ist_inv_plus_zero_dx (n) (c1) (c2): 𝐓❨n,c1 + c2❩ → 𝐓❨𝟎,c2❩ → 𝐓❨n,c1❩. #n #c1 #c2 #H #H2 elim (rtc_ist_inv_plus … H) -H #n1 #n2 #Hn1 #Hn2 #H destruct // qed-. lemma rtc_ist_inv_plus_unit_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 (rtc_ist_inv_plus … H) -H #n1 #n2 #Hn1 #Hn2 #H destruct /2 width=3 by ex2_intro/ qed-. -lemma rtc_ist_inv_plus_zu_dx (n) (c): 𝐓❪n,c+𝟙𝟘❫ → ⊥. +lemma rtc_ist_inv_plus_zu_dx (n) (c): 𝐓❨n,c+𝟙𝟘❩ → ⊥. #n #c #H elim (rtc_ist_inv_plus … H) -H #n1 #n2 #_ #H #_ /2 width=2 by rtc_ist_inv_uz/