X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Flib%2Farith.ma;h=dad1f938241812ef41928b983c6cb984f5ae5f2d;hb=89ea663d91904f483f8248cfaeaed5eda8715da2;hp=83322f4d8de57107b0eeb097bb7cd96d3cd83d86;hpb=9a6cf8c3b53fe33515acd1aef8e7c7a10d71ae71;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma index 83322f4d8..dad1f9382 100644 --- a/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma +++ b/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma @@ -96,6 +96,20 @@ qed. lemma arith_i: ∀x,y,z. y < x → x+z-y-1 = x-y-1+z. /2 width=1 by plus_minus/ qed-. +lemma idempotent_max: ∀n:nat. n = (n ∨ n). +#n normalize >le_to_leb_true // +qed. + +lemma associative_max: associative … max. +#x #y #z normalize +@(leb_elim x y) normalize #Hxy +@(leb_elim y z) normalize #Hyz // +[1,2: >le_to_leb_true /2 width=3 by transitive_le/ +| >not_le_to_leb_false /4 width=3 by lt_to_not_le, not_le_to_lt, transitive_lt/ + >not_le_to_leb_false // +] +qed. + (* Properties ***************************************************************) lemma eq_nat_dec: ∀n1,n2:nat. Decidable (n1 = n2).