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Simplified some proofs and made them work for new hyp_subst_tac.

expandshort

Deleted some useless things and made proofs of
refl_comp_subset and comp_equivI more like the versions in ZF/EquivClass.ML

Simplified using pattern replacements.

adjusted HOLCF for new hyp_subst_tac

Defined vv1 using let. Introduced gg1, gg2.

Deleted subset_imp_Un_Diff_eq, as it is identical to
Diff_partition. Used split_tac (sometimes via simplifier) to apply expand_if.
Replaced lt_oadd_disj1 by lt_oadd_odiff_disj, using ordinal difference instead
of a description. Removed the outer quantifier from all_sum_lepoll_m,
all_sum_lepoll_m_2. Changed all "lesspoll succ(m)" to "lepoll m" and
simplified proofs. Changed definitions of vv1 and ww1 to use lepoll instead
of lesspoll; therefore vv1(f,b,succ(m)) becomes vv1(f,b,m). Moved proof of
vv1_not_0 into the body of the proof using this result. Renamed variable aa
to s. Simplified lemma_iv using addss. Renamed some theorems; combined some
proofs.

New root file

Redefined OUnion in a definitional manner

Redefined OUnion in a definitional manner, and proved the
rules again. Deleted the rules OUnionI/E as they were not needed. Proved
OUN_cong. Extended OrdQuant_ss with oex_cong and defined Ord_atomize to
extract rewrite rules from ALL x<i... assumptions.