From 9e7db2554d0fd904966c0e6988f1c8763dd15a0b Mon Sep 17 00:00:00 2001 From: Claudio Sacerdoti Coen Date: Thu, 20 Mar 2008 20:39:28 +0000 Subject: [PATCH] Script fixed (it did not compile due to a mistake before committing). --- .../matita/library/demo/power_derivative.ma | 76 +------------------ 1 file changed, 4 insertions(+), 72 deletions(-) diff --git a/helm/software/matita/library/demo/power_derivative.ma b/helm/software/matita/library/demo/power_derivative.ma index 4f1b44000..fd58c9564 100644 --- a/helm/software/matita/library/demo/power_derivative.ma +++ b/helm/software/matita/library/demo/power_derivative.ma @@ -323,75 +323,7 @@ theorem derivative_power': ∀n:nat. D[x \sup (1+n)] = (1+n) · x \sup n. = (D[x] · x \sup (1+m) + x · D[x \sup (1+m)]). = (x \sup (1+m) + x · (costante (1+m) · x \sup m)). = (x \sup (1+m) + costante (1+m) · x \sup (1+m)). - - - - conclude (x \sup (1+m) + costante (1+m) · x \sup (1+m)) - = (costante 1 · x \sup (1+m) + costante (1+m) ·(x) \sup (1+m)) proof. - by (Fmult_one_f ((x)\sup(1+m))) - we proved (costante 1·(x)\sup(1+m)=(x)\sup(1+m)) (previous). - by (eq_OF_eq ? ? (λfoo:(R→R).foo+costante (1+m)·(x)\sup(1+m)) (costante 1 - ·(x)\sup(1 - +m)) ((x)\sup(1 - +m)) previous) - done. - = ((x)\sup(1+m)·costante 1+costante (1+m)·(x)\sup(1+m)) proof. - by (Fmult_commutative (costante 1) ((x)\sup(1+m))) - we proved (costante 1·(x)\sup(1+m)=(x)\sup(1+m)·costante 1) (previous). - by (eq_f ? ? (λfoo:(R→R).foo+costante (1+m)·(x)\sup(1+m)) (costante 1 - ·(x)\sup(1+m)) ((x)\sup(1 - +m) - ·costante - 1) previous) - done. - = ((x)\sup(1+m)·costante 1+(x)\sup(1+m)·costante (1+m)) proof. - by (Fmult_commutative ((x)\sup(1+m)) (costante (1+m))) - we proved ((x)\sup(1+m)·costante (1+m)=costante (1+m)·(x)\sup(1+m)) - - (previous) - . - by (eq_OF_eq ? ? (λfoo:(R→R).(x)\sup(1+m)·costante 1+foo) ((x)\sup(1+m) - ·costante - (1+m)) (costante - (1 - +m) - ·(x)\sup(1 - +m)) previous) - done. - = ((x)\sup(1+m)·(costante 1+costante (1+m))) proof. - by (Fmult_Fplus_distr ((x)\sup(1+m)) (costante 1) (costante (1+m))) - we proved - ((x)\sup(1+m)·(costante 1+costante (1+m)) - =(x)\sup(1+m)·costante 1+(x)\sup(1+m)·costante (1+m)) - - (previous) - . - by (sym_eq ? ((x)\sup(1+m)·(costante 1+costante (1+m))) ((x)\sup(1+m) - ·costante 1 - +(x)\sup(1+m) - ·costante (1+m)) previous) - done. - = ((costante 1+costante (1+m))·(x)\sup(1+m)) - exact (Fmult_commutative ((x)\sup(1+m)) (costante 1+costante (1+m))). - = (costante (1+(1+m))·(x)\sup(1+m)) proof. - by (costante_sum 1 (1+m)) - we proved (costante 1+costante (1+m)=costante (1+(1+m))) (previous). - by (eq_f ? ? (λfoo:(R→R).foo·(x)\sup(1+m)) (costante 1+costante (1+m)) (costante - (1 - +(1 - +m))) previous) - done. - = (costante (1+1+m)·(x)\sup(1+m)) proof. - by (assoc_plus 1 1 m) - we proved (1+1+m=1+(1+m)) (previous). - by (eq_OF_eq ? ? (λfoo:nat.costante foo·(x)\sup(1+m)) ? ? previous) - done. - = (costante (2+m)·(x)\sup(1+m)) proof done. - by (plus_n_SO 1) - we proved (2=1+1) (previous). - by (eq_OF_eq ? ? (λfoo:nat.costante (foo+m)·(x)\sup(1+m)) ? ? previous) - done. - - -(* end auto($Revision: 8206 $) proof: TIME=0.06 SIZE=100 DEPTH=100 *) done. -qed. + = ((2+m) · x \sup (1+m)) by Fmult_one_f Fmult_commutative + Fmult_Fplus_distr assoc_plus plus_n_SO costante_sum + done. +qed. \ No newline at end of file -- 2.39.2