Commit f2df0ef6 by MARCHE Claude

### update Isabelle realizations after changes in int.Exponentiation

parent 67d281ae
 ... @@ -154,7 +154,7 @@ why3_vc Mod_mult using assms by (simp add: emod_def add.commute) ... @@ -154,7 +154,7 @@ why3_vc Mod_mult using assms by (simp add: emod_def add.commute) why3_vc Mod_bound using assms by (simp_all add: emod_def) why3_vc Mod_bound using assms by (simp_all add: emod_def) why3_vc Div_unique using assms why3_vc Div_unique using assms proof - proof - have h0: "y \ 0" using assms by auto have h0: "y \ 0" using assms by auto have h1: "x = y * (x ediv y) + (x emod y)" using h0 Div_mod by blast have h1: "x = y * (x ediv y) + (x emod y)" using h0 Div_mod by blast have h2: "0 \ x emod y \ x emod y < y" using assms H1 h0 Mod_bound zabs_def have h2: "0 \ x emod y \ x emod y < y" using assms H1 h0 Mod_bound zabs_def ... @@ -166,16 +166,16 @@ why3_vc Div_unique using assms ... @@ -166,16 +166,16 @@ why3_vc Div_unique using assms assume a:"q < x ediv y" assume a:"q < x ediv y" have h5: "x ediv y \ q + 1" using a by linarith have h5: "x ediv y \ q + 1" using a by linarith have h6: "y * (x ediv y) >= y * (q + 1)" by (metis H1 h5 le_less mult_left_mono) have h6: "y * (x ediv y) >= y * (q + 1)" by (metis H1 h5 le_less mult_left_mono) have h7: "y * (x ediv y) >= q * y + y" by (metis Comm1 Mul_distr_l h6 monoid_mult_class.mult.right_neutral) have h7: "y * (x ediv y) >= q * y + y" by (metis Comm1 Mul_distr_l h6 monoid_mult_class.mult.right_neutral) thus "x ediv y = q" using H3 h1 h2 h7 by linarith thus "x ediv y = q" using H3 h1 h2 h7 by linarith next next assume a:"\ q < x ediv y" assume a:"\ q < x ediv y" show "x ediv y = q" show "x ediv y = q" proof (cases "x ediv y < q") proof (cases "x ediv y < q") assume b:"x ediv y < q" assume b:"x ediv y < q" have h5: "x ediv y \ q - 1" using b by linarith have h5: "x ediv y \ q - 1" using b by linarith have h6: "y * (x ediv y) <= y * (q - 1)" by (metis H1 h5 le_less mult_left_mono) have h6: "y * (x ediv y) <= y * (q - 1)" by (metis H1 h5 le_less mult_left_mono) have h7: "y * (x ediv y) <= q * y - y" by (metis Comm1 h6 int_distrib(4) monoid_mult_class.mult.right_neutral) have h7: "y * (x ediv y) <= q * y - y" by (metis Comm1 h6 int_distrib(4) monoid_mult_class.mult.right_neutral) thus "x ediv y = q" using H2 h3 h7 by linarith thus "x ediv y = q" using H2 h3 h7 by linarith next next assume b:"\ x ediv y < q" assume b:"\ x ediv y < q" ... @@ -320,7 +320,9 @@ why3_vc Power_sum using assms by (simp add: nat_add_distrib power_add) ... @@ -320,7 +320,9 @@ why3_vc Power_sum using assms by (simp add: nat_add_distrib power_add) why3_vc Power_mult using assms by (simp add: nat_mult_distrib power_mult) why3_vc Power_mult using assms by (simp add: nat_mult_distrib power_mult) why3_vc Power_mult2 by (simp add: power_mult_distrib) why3_vc Power_comm1 by (simp add: power_mult_distrib) why3_vc Power_comm2 by (simp add: power_mult_distrib) why3_vc Power_non_neg using assms by simp why3_vc Power_non_neg using assms by simp ... @@ -329,4 +331,3 @@ why3_vc Power_monotonic using assms by (simp add: power_increasing) ... @@ -329,4 +331,3 @@ why3_vc Power_monotonic using assms by (simp add: power_increasing) why3_end why3_end end end
 ... @@ -285,7 +285,9 @@ why3_vc Power_mult ... @@ -285,7 +285,9 @@ why3_vc Power_mult using assms using assms by (simp add: nat_mult_distrib power_mult) by (simp add: nat_mult_distrib power_mult) why3_vc Power_mult2 by (simp only:Power.comm_monoid_mult_class.power_mult_distrib) why3_vc Power_comm1 by simp why3_vc Power_comm2 by (simp add: semiring_normalization_rules(30)) why3_vc Power_s_alt why3_vc Power_s_alt proof - proof - ... ...
 ... @@ -288,7 +288,9 @@ why3_vc Power_mult ... @@ -288,7 +288,9 @@ why3_vc Power_mult using assms using assms by (simp add: nat_mult_distrib power_mult) by (simp add: nat_mult_distrib power_mult) why3_vc Power_mult2 by (simp only:Power.comm_monoid_mult_class.power_mult_distrib) why3_vc Power_comm1 by simp why3_vc Power_comm2 by (simp add: semiring_normalization_rules(30)) why3_vc Power_s_alt why3_vc Power_s_alt proof - proof - ... ...
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