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Commit 2021-09-30 20:25 64bcb389

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feat(order/succ_pred): define successor orders (#9397) A successor order is an order in which every (non maximal) element has a least greater element. A predecessor order is an order in which every (non minimal) element has a greatest smaller element. Typical examples are , ℕ+, , fin n, ordinal. Anytime you want to turn a < b + 1 into a ≤ b or a < b into a + 1 ≤ b, you want a succ_order.

Estimated changes

added theorem pred_order.le_pred_iff
added theorem pred_order.pred_bot
added theorem pred_order.pred_lt
added theorem pred_order.pred_lt_iff
added theorem pred_order.pred_lt_top
added theorem pred_order.pred_mono
added theorem pred_order.pred_ne_top
added theorem succ_order.bot_lt_succ
added theorem succ_order.lt_succ
added theorem succ_order.lt_succ_iff
added theorem succ_order.succ_le_iff
added theorem succ_order.succ_mono
added theorem succ_order.succ_ne_bot
added theorem succ_order.succ_top