test.ML

Added weak congruence rules to HOL: if_weak_cong, case_weak_cong,
split_weak_cong, nat_case_weak_cong, nat_rec_weak_cong. Used in llist.ML
to make simplifications faster.

HOL/gfp: re-ordered premises to put mono(f) early (first or right after
A==gfp(f) in the def_ rules). Renamed some variables in rules, A to X and
h to A. Renamed coinduct to weak_coinduct, coinduct2 to coinduct.
Strengthened coinduct as suggested by j. Frost, to have the premise X <= f(X
Un gfp(f)).

HOL/llist: used stronger coinduct rule to strengthen LList_coinduct,
LList_equalityI, llist_equalityI, llist_fun_equalityI and to delete the "2"
form of those rules. Proved List_Fun_LList_I, LListD_Fun_diag_I and
llistD_Fun_range_I to help use the new coinduction rules; most proofs
involving them required small changes. Proved prod_fun_range_eq_diag as
lemma for llist_equalityI.

let
 fun tac ss = resolve_tac(prems_of_ss ss) ORELSE' asm_simp_tac ss;
 val ss = set_prove_tac(HOL_ss addsimps [Suc_lessD],tac)
in prove_goal Nat.thy "!!x. Suc(Suc(Suc(x)))<y ==> x<y"
     (fn _ => [asm_simp_tac ss 1])
end;