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[Merged by Bors] - feat(data/fin): Add pred_{le,lt}_pred_iff #5121

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[Merged by Bors] - feat(data/fin): Add pred_{le,lt}_pred_iff #5121

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6e2f915
feat(data/fin): Add pred_{le,lt}_pred_iff
eric-wieser Nov 26, 2020
23bc6d8
Update src/data/fin.lean
eric-wieser Nov 26, 2020
a09a498
Update fin.lean
eric-wieser Nov 26, 2020
e675920
Update src/data/fin.lean
eric-wieser Nov 27, 2020
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6 changes: 6 additions & 0 deletions src/data/fin.lean
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Expand Up @@ -274,6 +274,12 @@ by { simp only [le_iff_coe_le_coe, coe_succ], exact ⟨le_of_succ_le_succ, succ_
@[simp] lemma succ_lt_succ_iff : a.succ < b.succ ↔ a < b :=
by { simp only [lt_iff_coe_lt_coe, coe_succ], exact ⟨lt_of_succ_lt_succ, succ_lt_succ⟩ }

@[simp] lemma pred_le_pred_iff {n : ℕ} {a b : fin n.succ} {ha hb} : a.pred ha ≤ b.pred hb ↔ b ≤ b :=
by rw [←succ_le_succ_iff, succ_pred, succ_pred]

@[simp] lemma pred_lt_pred_iff {n : ℕ} {a b : fin n.succ} {ha hb} : a.pred ha < b.pred hb ↔ b < b :=
by rw [←succ_lt_succ_iff, succ_pred, succ_pred]
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lemma succ_injective (n : ℕ) : injective (@fin.succ n) :=
λa b, succ.inj

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