c45a6a93f9
First part of #5015, using emoji variant of unicode symbols for ✅️,❌️,💥️. --- (Partially) closes #5015
78 lines
2.7 KiB
Text
78 lines
2.7 KiB
Text
theorem le_of_not_lt {a b : Nat} (_: ¬ a < b): b ≤ a := sorry
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theorem lt_of_succ_lt (_: a + 1 < b): a < b := sorry
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theorem succ_pred_eq_of_pos (_: 0 < v): v - 1 + 1 = v := sorry
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set_option trace.Meta.Tactic.simp true
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--set_option trace.Debug.Meta.Tactic.simp true
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/--
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warning: declaration uses 'sorry'
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---
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info: [Meta.Tactic.simp.rewrite] h₁:1000, k ≤ v - 1 ==> True
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[Meta.Tactic.simp.discharge] succ_pred_eq_of_pos discharge ✅️
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0 < v
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[Meta.Tactic.simp.rewrite] h₂:1000, 0 < v ==> True
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[Meta.Tactic.simp.rewrite] succ_pred_eq_of_pos:1000, v - 1 + 1 ==> v
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[Meta.Tactic.simp.rewrite] ite_true:1000, if True then ⟨v, ⋯⟩ else ⟨v - 1, ⋯⟩ ==> ⟨v, ⋯⟩
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[Meta.Tactic.simp.rewrite] eq_self:1000, ⟨v, ⋯⟩ = ⟨v, ⋯⟩ ==> True
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-/
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#guard_msgs in
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example (h₁: k ≤ v - 1) (h₂: 0 < v):
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(if k ≤ v - 1 then Fin.mk (v-1+1) sorry else Fin.mk (v-1) sorry) = Fin.mk v sorry (n:=n) := by
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simp only [
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h₁, h₂,
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ite_true,
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succ_pred_eq_of_pos
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----------------
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, le_of_not_lt
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, lt_of_succ_lt
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]
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-- it works
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/--
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warning: declaration uses 'sorry'
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---
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info: [Meta.Tactic.simp.rewrite] h₁:1000, k ≤ v - 1 ==> True
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[Meta.Tactic.simp.discharge] succ_pred_eq_of_pos discharge ✅️
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0 < v
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[Meta.Tactic.simp.rewrite] h₂:1000, 0 < v ==> True
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[Meta.Tactic.simp.rewrite] succ_pred_eq_of_pos:1000, v - 1 + 1 ==> v
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[Meta.Tactic.simp.rewrite] ite_true:1000, if True then ⟨v, ⋯⟩ else ⟨v - 1, ⋯⟩ ==> ⟨v, ⋯⟩
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[Meta.Tactic.simp.rewrite] eq_self:1000, ⟨v, ⋯⟩ = ⟨v, ⋯⟩ ==> True
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-/
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#guard_msgs in
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example (h₁: k ≤ v - 1) (h₂: 0 < v):
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(if k ≤ v - 1 then Fin.mk (v-1+1) sorry else Fin.mk (v-1) sorry) = Fin.mk v sorry (n:=n) := by
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simp (config := { memoize := false}) only [
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h₁, h₂,
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ite_true,
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succ_pred_eq_of_pos
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----------------
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, le_of_not_lt
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, lt_of_succ_lt
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]
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/--
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warning: declaration uses 'sorry'
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---
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info: [Meta.Tactic.simp.rewrite] h₁:1000, k ≤ v - 1 ==> True
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[Meta.Tactic.simp.discharge] succ_pred_eq_of_pos discharge ✅️
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0 < v
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[Meta.Tactic.simp.rewrite] h₂:1000, 0 < v ==> True
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[Meta.Tactic.simp.rewrite] succ_pred_eq_of_pos:1000, v - 1 + 1 ==> v
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[Meta.Tactic.simp.rewrite] ite_true:1000, if True then ⟨v, ⋯⟩ else ⟨v - 1, ⋯⟩ ==> ⟨v, ⋯⟩
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[Meta.Tactic.simp.rewrite] eq_self:1000, ⟨v, ⋯⟩ = ⟨v, ⋯⟩ ==> True
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-/
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#guard_msgs in
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example (h₁: k ≤ v - 1) (h₂: 0 < v):
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(if k ≤ v - 1 then Fin.mk (v-1+1) sorry else Fin.mk (v-1) sorry) = Fin.mk v sorry (n:=n) := by
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simp only [
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h₁, h₂,
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ite_true,
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succ_pred_eq_of_pos
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----------------
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--, le_of_not_lt
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--, lt_of_succ_lt
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]
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