src/HOL/AxClasses/Lattice/LatMorph.ML
author paulson
Wed Nov 05 13:23:46 1997 +0100 (1997-11-05)
changeset 4153 e534c4c32d54
parent 4091 771b1f6422a8
child 5069 3ea049f7979d
permissions -rw-r--r--
Ran expandshort, especially to introduce Safe_tac
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open LatMorph;
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(** monotone functions vs. "&&"- / "||"-semi-morphisms **)
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goalw thy [is_mono_def] "is_mono f = (ALL x y. f (x && y) [= f x && f y)";
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  by Safe_tac;
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  (*==> (level 1)*)
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    by (stac le_inf_eq 1);
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    by (rtac conjI 1);
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    by (Step_tac 1);
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    by (Step_tac 1);
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    by (etac mp 1);
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    by (rtac inf_lb1 1);
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    by (Step_tac 1);
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    by (Step_tac 1);
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    by (etac mp 1);
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    by (rtac inf_lb2 1);
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  (*==> (level 11)*)
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    by (rtac (conjI RS (le_trans RS mp)) 1);
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    by (rtac inf_lb2 2);
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    by (subgoal_tac "x && y = x" 1);
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    by (etac subst 1);
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    by (Fast_tac 1);
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    by (stac inf_connect 1);
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    by (assume_tac 1);
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qed "mono_inf_eq";
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goalw thy [is_mono_def] "is_mono f = (ALL x y. f x || f y [= f (x || y))";
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  by Safe_tac;
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  (*==> (level 1)*)
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    by (stac ge_sup_eq 1);
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    by (rtac conjI 1);
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    by (Step_tac 1);
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    by (Step_tac 1);
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    by (etac mp 1);
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    by (rtac sup_ub1 1);
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    by (Step_tac 1);
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    by (Step_tac 1);
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    by (etac mp 1);
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    by (rtac sup_ub2 1);
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  (*==> (level 11)*)
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    by (rtac (conjI RS (le_trans RS mp)) 1);
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    by (rtac sup_ub1 1);
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    by (subgoal_tac "x || y = y" 1);
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    by (etac subst 1);
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    by (Fast_tac 1);
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    by (stac sup_connect 1);
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    by (assume_tac 1);
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qed "mono_sup_eq";
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