X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Frelocation%2Fpr_nat_nat.ma;h=cfba24b077b43cc774bd4c86a18f2f377166468a;hb=15a2da1b45b2fd34ac67dcb58fc4b94330d18a93;hp=481ff1517b32ba7b414dd34db594ea48217ab985;hpb=6e4f8f6dc7ab7cdc0d9d852f6786947d3c4513cc;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/pr_nat_nat.ma b/matita/matita/contribs/lambdadelta/ground/relocation/pr_nat_nat.ma index 481ff1517..cfba24b07 100644 --- a/matita/matita/contribs/lambdadelta/ground/relocation/pr_nat_nat.ma +++ b/matita/matita/contribs/lambdadelta/ground/relocation/pr_nat_nat.ma @@ -20,7 +20,7 @@ include "ground/relocation/pr_nat.ma". (* Main destructions ********************************************************) theorem pr_nat_monotonic (k2) (l2) (f): - @↑❨l2,f❩ ≘ k2 → ∀k1,l1. @↑❨l1,f❩ ≘ k1 → l1 < l2 → k1 < k2. + @§❨l2,f❩ ≘ k2 → ∀k1,l1. @§❨l1,f❩ ≘ k1 → l1 < l2 → k1 < k2. #k2 @(nat_ind_succ … k2) -k2 [ #l2 #f #H2f elim (pr_nat_inv_zero_dx … H2f) -H2f // #g #H21 #_ #k1 #l1 #_ #Hi destruct @@ -37,7 +37,7 @@ theorem pr_nat_monotonic (k2) (l2) (f): qed-. theorem pr_nat_inv_monotonic (k1) (l1) (f): - @↑❨l1,f❩ ≘ k1 → ∀k2,l2. @↑❨l2,f❩ ≘ k2 → k1 < k2 → l1 < l2. + @§❨l1,f❩ ≘ k1 → ∀k2,l2. @§❨l2,f❩ ≘ k2 → k1 < k2 → l1 < l2. #k1 @(nat_ind_succ … k1) -k1 [ #l1 #f #H1f elim (pr_nat_inv_zero_dx … H1f) -H1f // #g * -l1 #H #k2 #l2 #H2f #Hk @@ -59,14 +59,14 @@ theorem pr_nat_inv_monotonic (k1) (l1) (f): qed-. theorem pr_nat_mono (f) (l) (l1) (l2): - @↑❨l,f❩ ≘ l1 → @↑❨l,f❩ ≘ l2 → l2 = l1. + @§❨l,f❩ ≘ l1 → @§❨l,f❩ ≘ l2 → l2 = l1. #f #l #l1 #l2 #H1 #H2 elim (nat_split_lt_eq_gt l2 l1) // #Hi elim (nlt_ge_false l l) /2 width=6 by pr_nat_inv_monotonic/ qed-. theorem pr_nat_inj (f) (l1) (l2) (l): - @↑❨l1,f❩ ≘ l → @↑❨l2,f❩ ≘ l → l1 = l2. + @§❨l1,f❩ ≘ l → @§❨l2,f❩ ≘ l → l1 = l2. #f #l1 #l2 #l #H1 #H2 elim (nat_split_lt_eq_gt l2 l1) // #Hi elim (nlt_ge_false l l) /2 width=6 by pr_nat_monotonic/