X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fdemo%2Fpower_derivative.ma;fp=helm%2Fsoftware%2Fmatita%2Flibrary%2Fdemo%2Fpower_derivative.ma;h=8ab638da8694fe04a6c82d280f12ef7233155e5b;hb=aa5f71baeba0299c0d29be01798f7a1ad13656f9;hp=e8ab55c3595108eb3e08a8d60c49819752831832;hpb=4ccc7ef7fe3d43fb0f882768d2818a54e24c8857;p=helm.git diff --git a/helm/software/matita/library/demo/power_derivative.ma b/helm/software/matita/library/demo/power_derivative.ma index e8ab55c35..8ab638da8 100644 --- a/helm/software/matita/library/demo/power_derivative.ma +++ b/helm/software/matita/library/demo/power_derivative.ma @@ -40,11 +40,7 @@ interpretation "None" 'one = interpretation "Rplus" 'plus x y = (cic:/matita/demo/power_derivative/Rplus.con x y). -notation "hvbox(a break \middot b)" - left associative with precedence 55 -for @{ 'times $a $b }. - -interpretation "Rmult" 'times x y = +interpretation "Rmult" 'middot x y = (cic:/matita/demo/power_derivative/Rmult.con x y). definition Fplus ≝ @@ -55,7 +51,7 @@ definition Fmult ≝ interpretation "Fplus" 'plus x y = (cic:/matita/demo/power_derivative/Fplus.con x y). -interpretation "Fmult" 'times x y = +interpretation "Fmult" 'middot x y = (cic:/matita/demo/power_derivative/Fmult.con x y). notation "2" with precedence 89 @@ -93,13 +89,13 @@ coercion inj. axiom Rplus_Rzero_x: ∀x:R.0+x=x. axiom Rplus_comm: symmetric ? Rplus. axiom Rplus_assoc: associative ? Rplus. -axiom Rmult_Rone_x: ∀x:R.1*x=x. -axiom Rmult_Rzero_x: ∀x:R.0*x=0. +axiom Rmult_Rone_x: ∀x:R.1 · x=x. +axiom Rmult_Rzero_x: ∀x:R.0 · x=0. axiom Rmult_assoc: associative ? Rmult. axiom Rmult_comm: symmetric ? Rmult. axiom Rmult_Rplus_distr: distributive ? Rmult Rplus. -alias symbol "times" = "Rmult". +alias symbol "middot" = "Rmult". alias symbol "plus" = "natural plus". definition monomio ≝ @@ -245,7 +241,7 @@ axiom derivative_x0: D[x \sup 0] = 0. axiom derivative_x1: D[x] = 1. axiom derivative_mult: ∀f,g:R→R. D[f·g] = D[f]·g + f·D[g]. -alias symbol "times" = "Fmult". +alias symbol "middot" = "Fmult". theorem derivative_power: ∀n:nat. D[x \sup n] = n·x \sup (pred n). assume n:nat.