15 lines
725 B
Text
15 lines
725 B
Text
/-
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This test ensures `simp` will not try to synthesize instance implicit arguments when they can
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be inferred by unification. Note that in some cases the inferred instance may not even be
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definitionally equal to the inferred one, and would prevent the [simp] theorem from being applied.
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-/
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theorem dec_and (p q : Prop) [Decidable (p ∧ q)] [Decidable p] [Decidable q] : decide (p ∧ q) = (p && q) := by
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by_cases p <;> by_cases q <;> simp [*]
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theorem dec_not (p : Prop) [Decidable (¬p)] [Decidable p] : decide (¬p) = !p := by
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by_cases p <;> simp [*]
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example [Decidable u] [Decidable v] : decide (u ∧ (v → False)) = (decide u && !decide v) := by
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simp only [imp_false]
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simp only [dec_and]
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simp only [dec_not]
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