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Commit 2022-08-11 05:59 60a1dcf7

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refactor(set_theory/ordinal/cantor_normal_form): simplify CNF definition (#15449) We simplify the definition of CNF by removing the casing on b = 0. Note that the new definition is not equivalent to the old one: we now have CNF 0 o = [(0, o)] instead of CNF 0 o = []. This is a good thing though, since it means that CNF_foldr (arguably the defining characteristic of the CNF) is now unconditionally true. We generalize previously existing theorems according to this new definition. Note that none of the theorems have had their hypotheses strengthened, but a few have been weakened.

Estimated changes

modified theorem ordinal.CNF_foldr
modified theorem ordinal.CNF_fst_le
modified theorem ordinal.CNF_fst_le_log
modified theorem ordinal.CNF_lt_snd
modified theorem ordinal.CNF_ne_zero
added theorem ordinal.CNF_of_le_one
added theorem ordinal.CNF_of_lt
deleted theorem ordinal.CNF_pairwise
deleted theorem ordinal.CNF_rec_ne_zero
added theorem ordinal.CNF_rec_pos
modified theorem ordinal.CNF_rec_zero
modified theorem ordinal.CNF_snd_lt
modified theorem ordinal.CNF_zero
modified theorem ordinal.one_CNF
modified theorem ordinal.zero_CNF