--- a/src/ZF/UNITY/Increasing.ML Tue Jul 08 11:44:30 2003 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,229 +0,0 @@
-(* Title: ZF/UNITY/GenIncreasing
- ID: $Id \\<in> Increasing.ML,v 1.3 2003/06/27 16:40:25 paulson Exp $
- Author: Sidi O Ehmety, Cambridge University Computer Laboratory
- Copyright 1998 University of Cambridge
-
-A general form of the `Increasing' relation of Charpentier
-*)
-
-(** increasing **)
-
-Goalw [increasing_def] "increasing[A](r, f) <= program";
-by (Blast_tac 1);
-qed "increasing_type";
-
-Goalw [increasing_def] "F \\<in> increasing[A](r, f) ==> F \\<in> program";
-by (Blast_tac 1);
-qed "increasing_into_program";
-
-Goalw [increasing_def]
-"[| F \\<in> increasing[A](r, f); x \\<in> A |] ==>F \\<in> stable({s \\<in> state. <x, f(s)>:r})";
-by (Blast_tac 1);
-qed "increasing_imp_stable";
-
-Goalw [increasing_def]
-"F \\<in> increasing[A](r,f) ==> F \\<in> program & (\\<exists>a. a \\<in> A) & (\\<forall>s \\<in> state. f(s):A)";
-by (subgoal_tac "\\<exists>x. x \\<in> state" 1);
-by (auto_tac (claset() addDs [stable_type RS subsetD]
- addIs [st0_in_state], simpset()));
-qed "increasingD";
-
-Goalw [increasing_def, stable_def]
- "F \\<in> increasing[A](r, %s. c) <-> F \\<in> program & c \\<in> A";
-by (subgoal_tac "\\<exists>x. x \\<in> state" 1);
-by (auto_tac (claset() addDs [stable_type RS subsetD]
- addIs [st0_in_state], simpset()));
-qed "increasing_constant";
-Addsimps [increasing_constant];
-
-Goalw [increasing_def, stable_def, part_order_def,
- constrains_def, mono1_def, metacomp_def]
-"[| mono1(A, r, B, s, g); refl(A, r); trans[B](s) |] ==> \
-\ increasing[A](r, f) <= increasing[B](s, g comp f)";
-by (Clarify_tac 1);
-by (Asm_full_simp_tac 1);
-by (Clarify_tac 1);
-by (subgoal_tac "xa \\<in> state" 1);
-by (blast_tac (claset() addSDs [ActsD]) 2);
-by (subgoal_tac "<f(xb), f(xb)>:r" 1);
-by (force_tac (claset(), simpset() addsimps [refl_def]) 2);
-by (rotate_tac 5 1);
-by (dres_inst_tac [("x", "f(xb)")] bspec 1);
-by (rotate_tac ~1 2);
-by (dres_inst_tac [("x", "act")] bspec 2);
-by (ALLGOALS(Asm_full_simp_tac));
-by (dres_inst_tac [("A", "act``?u"), ("c", "xa")] subsetD 1);
-by (Blast_tac 1);
-by (dres_inst_tac [("x", "f(xa)"), ("x1", "f(xb)")] (bspec RS bspec) 1);
-by (res_inst_tac [("b", "g(f(xb))"), ("A", "B")] trans_onD 3);
-by (ALLGOALS(Asm_simp_tac));
-qed "subset_increasing_comp";
-
-Goal "[| F \\<in> increasing[A](r, f); mono1(A, r, B, s, g); \
-\ refl(A, r); trans[B](s) |] ==> F \\<in> increasing[B](s, g comp f)";
-by (rtac (subset_increasing_comp RS subsetD) 1);
-by Auto_tac;
-qed "imp_increasing_comp";
-
-Goalw [increasing_def, Lt_def]
- "increasing[nat](Le, f) <= increasing[nat](Lt, f)";
-by Auto_tac;
-qed "strict_increasing";
-
-Goalw [increasing_def, Gt_def, Ge_def]
- "increasing[nat](Ge, f) <= increasing[nat](Gt, f)";
-by Auto_tac;
-by (etac natE 1);
-by (auto_tac (claset(), simpset() addsimps [stable_def]));
-qed "strict_gt_increasing";
-
-(** Increasing **)
-
-Goalw [increasing_def, Increasing_def]
- "F \\<in> increasing[A](r, f) ==> F \\<in> Increasing[A](r, f)";
-by (auto_tac (claset() addIs [stable_imp_Stable], simpset()));
-qed "increasing_imp_Increasing";
-
-Goalw [Increasing_def] "Increasing[A](r, f) <= program";
-by Auto_tac;
-qed "Increasing_type";
-
-Goalw [Increasing_def] "F \\<in> Increasing[A](r, f) ==> F \\<in> program";
-by Auto_tac;
-qed "Increasing_into_program";
-
-Goalw [Increasing_def]
-"[| F \\<in> Increasing[A](r, f); a \\<in> A |] ==> F \\<in> Stable({s \\<in> state. <a,f(s)>:r})";
-by (Blast_tac 1);
-qed "Increasing_imp_Stable";
-
-Goalw [Increasing_def]
-"F \\<in> Increasing[A](r, f) ==> F \\<in> program & (\\<exists>a. a \\<in> A) & (\\<forall>s \\<in> state. f(s):A)";
-by (subgoal_tac "\\<exists>x. x \\<in> state" 1);
-by (auto_tac (claset() addIs [st0_in_state], simpset()));
-qed "IncreasingD";
-
-Goal
-"F \\<in> Increasing[A](r, %s. c) <-> F \\<in> program & (c \\<in> A)";
-by (subgoal_tac "\\<exists>x. x \\<in> state" 1);
-by (auto_tac (claset() addSDs [IncreasingD]
- addIs [st0_in_state,
- increasing_imp_Increasing], simpset()));
-qed "Increasing_constant";
-Addsimps [Increasing_constant];
-
-Goalw [Increasing_def, Stable_def, Constrains_def, part_order_def,
- constrains_def, mono1_def, metacomp_def]
-"[| mono1(A, r, B, s, g); refl(A, r); trans[B](s) |] ==> \
-\ Increasing[A](r, f) <= Increasing[B](s, g comp f)";
-by Safe_tac;
-by (ALLGOALS(asm_full_simp_tac (simpset() addsimps [ActsD])));
-by (subgoal_tac "xb \\<in> state & xa \\<in> state" 1);
-by (asm_simp_tac (simpset() addsimps [ActsD]) 2);
-by (subgoal_tac "<f(xb), f(xb)>:r" 1);
-by (force_tac (claset(), simpset() addsimps [refl_def]) 2);
-by (rotate_tac 5 1);
-by (dres_inst_tac [("x", "f(xb)")] bspec 1);
-by (ALLGOALS(Asm_full_simp_tac));
-by (Clarify_tac 1);
-by (rotate_tac ~2 1);
-by (dres_inst_tac [("x", "act")] bspec 1);
-by (dres_inst_tac [("A", "act``?u"), ("c", "xa")] subsetD 2);
-by (ALLGOALS(Asm_full_simp_tac));
-by (Blast_tac 1);
-by (dres_inst_tac [("x", "f(xa)"), ("x1", "f(xb)")] (bspec RS bspec) 1);
-by (res_inst_tac [("b", "g(f(xb))"), ("A", "B")] trans_onD 3);
-by (ALLGOALS(Asm_full_simp_tac));
-qed "subset_Increasing_comp";
-
-Goal "[| F \\<in> Increasing[A](r, f); mono1(A, r, B, s, g); refl(A, r); trans[B](s) |] \
-\ ==> F \\<in> Increasing[B](s, g comp f)";
-by (rtac (subset_Increasing_comp RS subsetD) 1);
-by Auto_tac;
-qed "imp_Increasing_comp";
-
-Goalw [Increasing_def, Lt_def]
-"Increasing[nat](Le, f) <= Increasing[nat](Lt, f)";
-by Auto_tac;
-qed "strict_Increasing";
-
-Goalw [Increasing_def, Ge_def, Gt_def]
-"Increasing[nat](Ge, f)<= Increasing[nat](Gt, f)";
-by Auto_tac;
-by (etac natE 1);
-by (auto_tac (claset(), simpset() addsimps [Stable_def]));
-qed "strict_gt_Increasing";
-
-(** Two-place monotone operations **)
-
-Goalw [increasing_def, stable_def,
- part_order_def, constrains_def, mono2_def]
-"[| F \\<in> increasing[A](r, f); F \\<in> increasing[B](s, g); \
-\ mono2(A, r, B, s, C, t, h); refl(A, r); refl(B, s); trans[C](t) |] ==> \
-\ F \\<in> increasing[C](t, %x. h(f(x), g(x)))";
-by (Clarify_tac 1);
-by (Asm_full_simp_tac 1);
-by (Clarify_tac 1);
-by (rename_tac "xa xb" 1);
-by (subgoal_tac "xb \\<in> state & xa \\<in> state" 1);
-by (blast_tac (claset() addSDs [ActsD]) 2);
-by (subgoal_tac "<f(xb), f(xb)>:r & <g(xb), g(xb)>:s" 1);
-by (force_tac (claset(), simpset() addsimps [refl_def]) 2);
-by (rotate_tac 6 1);
-by (dres_inst_tac [("x", "f(xb)")] bspec 1);
-by (rotate_tac 1 2);
-by (dres_inst_tac [("x", "g(xb)")] bspec 2);
-by (ALLGOALS(Asm_simp_tac));
-by (rotate_tac ~1 1);
-by (dres_inst_tac [("x", "act")] bspec 1);
-by (rotate_tac ~3 2);
-by (dres_inst_tac [("x", "act")] bspec 2);
-by (ALLGOALS(Asm_full_simp_tac));
-by (dres_inst_tac [("A", "act``?u"), ("c", "xa")] subsetD 1);
-by (dres_inst_tac [("A", "act``?u"), ("c", "xa")] subsetD 2);
-by (Blast_tac 1);
-by (Blast_tac 1);
-by (rotate_tac ~4 1);
-by (dres_inst_tac [("x", "f(xa)"), ("x1", "f(xb)")] (bspec RS bspec) 1);
-by (rotate_tac ~1 3);
-by (dres_inst_tac [("x", "g(xa)"), ("x1", "g(xb)")] (bspec RS bspec) 3);
-by (ALLGOALS(Asm_full_simp_tac));
-by (res_inst_tac [("b", "h(f(xb), g(xb))"), ("A", "C")] trans_onD 1);
-by (ALLGOALS(Asm_full_simp_tac));
-qed "imp_increasing_comp2";
-
-Goalw [Increasing_def, stable_def,
- part_order_def, constrains_def, mono2_def, Stable_def, Constrains_def]
-"[| F \\<in> Increasing[A](r, f); F \\<in> Increasing[B](s, g); \
-\ mono2(A, r, B, s, C, t, h); refl(A, r); refl(B, s); trans[C](t) |] ==> \
-\ F \\<in> Increasing[C](t, %x. h(f(x), g(x)))";
-by Safe_tac;
-by (ALLGOALS(asm_full_simp_tac (simpset() addsimps [ActsD])));
-by (subgoal_tac "xa \\<in> state & x \\<in> state" 1);
-by (blast_tac (claset() addSDs [ActsD]) 2);
-by (subgoal_tac "<f(xa), f(xa)>:r & <g(xa), g(xa)>:s" 1);
-by (force_tac (claset(), simpset() addsimps [refl_def]) 2);
-by (rotate_tac 6 1);
-by (dres_inst_tac [("x", "f(xa)")] bspec 1);
-by (rotate_tac 1 2);
-by (dres_inst_tac [("x", "g(xa)")] bspec 2);
-by (ALLGOALS(Asm_simp_tac));
-by (Clarify_tac 1);
-by (rotate_tac ~2 1);
-by (dres_inst_tac [("x", "act")] bspec 1);
-by (rotate_tac ~3 2);
-by (dres_inst_tac [("x", "act")] bspec 2);
-by (ALLGOALS(Asm_full_simp_tac));
-by (dres_inst_tac [("A", "act``?u"), ("c", "x")] subsetD 1);
-by (dres_inst_tac [("A", "act``?u"), ("c", "x")] subsetD 2);
-by (Blast_tac 1);
-by (Blast_tac 1);
-by (rotate_tac ~9 1);
-by (dres_inst_tac [("x", "f(x)"), ("x1", "f(xa)")] (bspec RS bspec) 1);
-by (rotate_tac ~1 3);
-by (dres_inst_tac [("x", "g(x)"), ("x1", "g(xa)")] (bspec RS bspec) 3);
-by (ALLGOALS(Asm_full_simp_tac));
-by (res_inst_tac [("b", "h(f(xa), g(xa))"), ("A", "C")] trans_onD 1);
-by (ALLGOALS(Asm_full_simp_tac));
-qed "imp_Increasing_comp2";
-