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Commit 2020-09-02 13:19 ddbdfeb5

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chore(data/fin): succ_above defn compares fin terms instead of values (#3999) fin.succ_above is redefined to use a comparison between two fin (n + 1) instead of their coerced values in nat. This should delay any "escape" from fin into nat until necessary. Lemmas are added regarding fin.succ_above. Some proofs for existing lemmas reworked for new definition and simplified. Additionally, docstrings are added for related lemmas. New lemmas: Comparison after embedding: succ_above_lt_ge succ_above_lt_gt Injectivity lemmas: succ_above_right_inj succ_above_right_injective succ_above_left_inj succ_above_left_injective finset lemma: fin.univ_succ_above prod and sum lemmas: fin.prod_univ_succ_above

Estimated changes

added theorem fin.cast_succ_pos
modified theorem fin.pred_above_succ_above
modified def fin.succ_above
modified theorem fin.succ_above_above
modified theorem fin.succ_above_below
modified theorem fin.succ_above_descend
added theorem fin.succ_above_lt_ge
added theorem fin.succ_above_lt_gt
modified theorem fin.succ_above_ne
modified theorem fin.prod_univ_cast_succ
modified theorem fin.prod_univ_succ
modified theorem fin.prod_univ_zero
modified theorem fin.sum_univ_cast_succ
modified theorem fin.sum_univ_succ