From 4c698212feffe7bb3119b62533a58132401668be Mon Sep 17 00:00:00 2001 From: Stefano Zacchiroli Date: Wed, 26 Jul 2006 09:24:55 +0000 Subject: [PATCH] added tinycals to the proof we frequently use for examples and screenshots --- matita/library/nat/factorization.ma | 35 ++++++++++++++--------------- 1 file changed, 17 insertions(+), 18 deletions(-) diff --git a/matita/library/nat/factorization.ma b/matita/library/nat/factorization.ma index 715a9795f..e61658786 100644 --- a/matita/library/nat/factorization.ma +++ b/matita/library/nat/factorization.ma @@ -169,24 +169,23 @@ match f with | nfa_one \Rightarrow (S O) | (nfa_proper g) \Rightarrow defactorize_aux g O]. -theorem lt_O_defactorize_aux: \forall f:nat_fact.\forall i:nat. -O < defactorize_aux f i. -intro.elim f.simplify.unfold lt. -rewrite > times_n_SO. -apply le_times. -change with (O < nth_prime i). -apply lt_O_nth_prime_n. -change with (O < exp (nth_prime i) n). -apply lt_O_exp. -apply lt_O_nth_prime_n. -simplify.unfold lt. -rewrite > times_n_SO. -apply le_times. -change with (O < exp (nth_prime i) n). -apply lt_O_exp. -apply lt_O_nth_prime_n. -change with (O < defactorize_aux n1 (S i)). -apply H. +theorem lt_O_defactorize_aux: + \forall f:nat_fact. + \forall i:nat. + O < defactorize_aux f i. +intro; elim f; +[1,2: + simplify; unfold lt; + rewrite > times_n_SO; + apply le_times; + [ change with (O < nth_prime i); + apply lt_O_nth_prime_n; + |2,3: + change with (O < exp (nth_prime i) n); + apply lt_O_exp; + apply lt_O_nth_prime_n; + | change with (O < defactorize_aux n1 (S i)); + apply H; ] ] qed. theorem lt_SO_defactorize_aux: \forall f:nat_fact.\forall i:nat. -- 2.39.2