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1440
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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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4091
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by (safe_tac (claset()));
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1440
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(*==> (level 1)*)
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by (stac le_inf_eq 1);
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br conjI 1;
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1899
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by (Step_tac 1);
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by (Step_tac 1);
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1440
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be mp 1;
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br inf_lb1 1;
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1899
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by (Step_tac 1);
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by (Step_tac 1);
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1440
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be mp 1;
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br inf_lb2 1;
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(*==> (level 11)*)
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br (conjI RS (le_trans RS mp)) 1;
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br inf_lb2 2;
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by (subgoal_tac "x && y = x" 1);
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be subst 1;
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1899
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by (Fast_tac 1);
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1440
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by (stac inf_connect 1);
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ba 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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4091
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by (safe_tac (claset()));
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1440
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(*==> (level 1)*)
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by (stac ge_sup_eq 1);
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br conjI 1;
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1899
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by (Step_tac 1);
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by (Step_tac 1);
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1440
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be mp 1;
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br sup_ub1 1;
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1899
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by (Step_tac 1);
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by (Step_tac 1);
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1440
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be mp 1;
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br sup_ub2 1;
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(*==> (level 11)*)
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br (conjI RS (le_trans RS mp)) 1;
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br sup_ub1 1;
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by (subgoal_tac "x || y = y" 1);
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be subst 1;
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1899
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by (Fast_tac 1);
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1440
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by (stac sup_connect 1);
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ba 1;
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qed "mono_sup_eq";
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