7fa1a8b114
This PR eliminates uses of `intros x y z` (with arguments) and updates the `intros` docstring to suggest that `intro x y z` should be used instead. The `intros` tactic is historical, and can be traced all the way back to Lean 2, when `intro` could only introduce a single hypothesis. Since 2020, the `intro` tactic has superceded it. The `intros` tactic (without arguments) is currently still useful.
124 lines
3.3 KiB
Text
124 lines
3.3 KiB
Text
private axiom test_sorry : ∀ {α}, α
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-- To see the (sorted) list of lemmas that `rw?` will try rewriting by, use:
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-- set_option trace.Tactic.rewrites.lemmas true
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/--
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info: Try this: rw [List.map_append]
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-- no goals
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-/
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#guard_msgs in
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example (f : α → β) (L M : List α) : (L ++ M).map f = L.map f ++ M.map f := by
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rw?
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/--
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info: Try this: rw [Nat.one_mul]
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-- no goals
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-/
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#guard_msgs in
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example (h : Nat) : 1 * h = h := by
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rw?
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#guard_msgs(drop info) in
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example (h : Int) (hyp : g * 1 = h) : g = h := by
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rw? at hyp
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assumption
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#guard_msgs(drop info) in
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example : ∀ (x y : Nat), x ≤ y := by
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intro x y
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rw? -- Used to be an error here https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/panic.20and.20error.20with.20rw.3F/near/370495531
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exact test_sorry
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example : ∀ (x y : Nat), x ≤ y := by
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-- Used to be a panic here https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/panic.20and.20error.20with.20rw.3F/near/370495531
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fail_if_success rw?
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exact test_sorry
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axiom K : Type
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@[instance] axiom K.hasOne : OfNat K 1
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@[instance] axiom K.hasIntCoe : Coe K Int
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noncomputable def foo : K → K := test_sorry
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#guard_msgs(drop info) in
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example : foo x = 1 ↔ ∃ k : Int, x = k := by
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rw? -- Used to panic, see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/panic.20and.20error.20with.20rw.3F/near/370598036
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exact test_sorry
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theorem six_eq_seven : 6 = 7 := test_sorry
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-- This test also verifies that we are removing duplicate results;
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-- it previously also reported `Nat.cast_ofNat`
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#guard_msgs(drop info) in
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example : ∀ (x : Nat), x ≤ 6 := by
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rw?
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guard_target = ∀ (x : Nat), x ≤ 7
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exact test_sorry
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#guard_msgs(drop info) in
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example : ∀ (x : Nat) (_w : x ≤ 6), x ≤ 8 := by
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rw?
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guard_target = ∀ (x : Nat) (_w : x ≤ 7), x ≤ 8
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exact test_sorry
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-- check we can look inside let expressions
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#guard_msgs(drop info) in
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example (n : Nat) : let y := 3; n + y = 3 + n := by
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rw?
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axiom α : Type
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axiom f : α → α
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axiom z : α
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axiom f_eq (n) : f n = z
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-- Check that the same lemma isn't used multiple times.
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-- This used to report two redundant copies of `f_eq`.
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-- It be lovely if `rw?` could produce two *different* rewrites by `f_eq` here!
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#guard_msgs(drop info) in
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theorem test : f n = f m := by
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fail_if_success rw? [-f_eq] -- Check that we can forbid lemmas.
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rw?
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rw [f_eq]
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-- Check that we can rewrite by local hypotheses.
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#guard_msgs(drop info) in
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example (h : 1 = 2) : 2 = 1 := by
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rw?
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def zero : Nat := 0
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-- This used to (incorrectly!) succeed because `rw?` would try `rfl`,
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-- rather than `withReducible` `rfl`.
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#guard_msgs(drop info) in
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example : zero = 0 := by
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rw?
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exact test_sorry
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-- Discharge side conditions from local hypotheses.
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/--
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info: Try this: rw [h p]
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-- no goals
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-/
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#guard_msgs in
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example {P : Prop} (p : P) (h : P → 1 = 2) : 2 = 1 := by
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rw?
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-- Use `solve_by_elim` to discharge side conditions.
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/--
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info: Try this: rw [h (f p)]
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-- no goals
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-/
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#guard_msgs in
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example {P Q : Prop} (p : P) (f : P → Q) (h : Q → 1 = 2) : 2 = 1 := by
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rw?
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-- Rewrite in reverse, discharging side conditions from local hypotheses.
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/--
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info: Try this: rw [← h₁ p]
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-- Q a
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-/
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#guard_msgs in
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example {P : Prop} (p : P) (Q : α → Prop) (a b : α) (h₁ : P → a = b) (w : Q a) : Q b := by
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rw?
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exact w
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