08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
73 lines
2 KiB
Text
73 lines
2 KiB
Text
/-!
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# Tests of the `congr` tactic
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-/
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example (h : a = b) : Nat.succ (a + 1) = Nat.succ (b + 1) := by
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congr
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example (h : a = b) : Nat.succ (a + 1) = Nat.succ (b + 1) := by
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congr 1
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show a + 1 = b + 1
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rw [h]
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def f (p : Prop) (a : Nat) (h : a > 0) [Decidable p] : Nat :=
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if p then
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a - 1
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else
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a + 1
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example (h : a = b) : f True (a + 1) (by simp +arith) = f (0 = 0) (b + 1) (by simp +arith) := by
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congr
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decide
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example (h : a = b) : f True (a + 1) (by simp +arith) = f (0 = 0) (b + 1) (by simp +arith) := by
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congr 1
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· decide
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· show a + 1 = b + 1
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rw [h]
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example (h₁ : α = β) (h₂ : α = γ) (a : α) : cast h₁ a ≍ cast h₂ a := by
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congr
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· subst h₁ h₂; rfl
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· subst h₁ h₂; apply heq_of_eq; rfl
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example (f : Nat → Nat) (g : Nat → Nat) : f (g (x + y)) = f (g (y + x)) := by
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congr 2
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rw [Nat.add_comm]
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example (p q r : Prop) (h : q = r) : (p → q) = (p → r) := by
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congr
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example (p q r s : Prop) (h₁ : q = r) (h₂ : r = s) : (p → q) = (p → s) := by
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congr
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rw [h₁, h₂]
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namespace Tao1
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/-!
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Reported on Zulip: https://leanprover.zulipchat.com/#narrow/channel/287929-mathlib4/topic/congr.20unexpectedly.20fails.20with.20Set.2Eimage/near/527382064
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The `congr` tactic used to make no progress here because `congr` was computing the arity from the head function
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(`Set.image`) rather than from the actual number of supplied arguments.
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-/
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def Set (α : Type _) := α → Prop
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def Set.image {α β : Type _} (f : α → β) (s : Set α) : Set β :=
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fun y => ∃ x, s x ∧ f x = y
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infixl:80 " '' " => Set.image
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example {X Y : Type} (f : X → Y) (E F : Set X) (h : E = F) : f '' E = f '' F := by
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congr
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/-!
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This also didn't work, for the same reason.
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-/
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example {X Y : Type} (f g : X → Y) (h : f = g) : Set.image f = Set.image g := by
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congr
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/-!
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The `HEq` version also did not work.
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-/
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example {X Y Y' : Type} (h : Y = Y') (f : X → Y) (f' : X → Y') (hf : f ≍ f') (E : Set X) : f '' E ≍ f' '' E := by
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congr
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end Tao1
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