3af9ab64ed
This PR adds a feature to the `subst` tactic so that when `x : X := v` is a local definition, `subst x` substitutes `v` for `x` in the goal and removes `x`. Previously the tactic would throw an error.
112 lines
1.8 KiB
Text
112 lines
1.8 KiB
Text
/-!
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# Tests of the `subst` tactic when `let`s are present.
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-/
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/-!
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Eliminates `a` even though `e : id a = m`.
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-/
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/--
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trace: case intro
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n : Nat
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m : Nat := n
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a : Nat
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e : id a = m
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⊢ 0 + n = n
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---
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trace: case intro
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a : Nat
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m : Nat := id a
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⊢ 0 + id a = id a
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-/
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#guard_msgs in
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theorem ex1 (n : Nat) : 0 + n = n := by
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let m := n
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have h : ∃ k, id k = m := ⟨m, rfl⟩
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cases h with
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| intro a e =>
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trace_state
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subst e
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trace_state
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apply Nat.zero_add
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/-!
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Eliminates `a` even though `e : m = id a`.
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-/
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/--
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trace: case intro
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n : Nat
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m : Nat := n
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a : Nat
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e : m = id a
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⊢ 0 + n = n
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---
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trace: case intro
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n : Nat
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m : Nat := n
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⊢ 0 + n = n
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-/
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#guard_msgs in
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theorem ex2 (n : Nat) : 0 + n = n := by
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let m := n
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have h : ∃ k, m = id k := ⟨m, rfl⟩
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cases h with
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| intro a e =>
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trace_state
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subst e
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trace_state
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apply Nat.zero_add
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/-!
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Since `v` is a let binding, the `subst v` tactic instead
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zeta delta reduces it everywhere and then clears it.
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-/
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/--
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trace: n : Nat
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h : n = 0
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m : Nat := n + 1
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v : Nat := m + 1
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this : v = n + 2
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⊢ 0 + n = 0
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---
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trace: n : Nat
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h : n = 0
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m : Nat := n + 1
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this : m + 1 = n + 2
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⊢ 0 + n = 0
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---
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trace: m : Nat := 0 + 1
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this : m + 1 = 0 + 2
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⊢ 0 + 0 = 0
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-/
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#guard_msgs in
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theorem ex3 (n : Nat) (h : n = 0) : 0 + n = 0 := by
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let m := n + 1
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let v := m + 1
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have : v = n + 2 := rfl
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trace_state
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subst v
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trace_state
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subst n
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trace_state
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rfl
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/-!
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Can't do `subst this` with `this : v = n + 2` since `v` is a let binding.
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The tactic sees `m + 1 = n + 2` and fails.
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-/
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/--
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error: tactic 'subst' failed, invalid equality proof, it is not of the form (x = t) or (t = x)
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v = n + 2
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n : Nat
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h : n = 0
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m : Nat := n + 1
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v : Nat := m + 1
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this : v = n + 2
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⊢ 0 + n = 0
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-/
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#guard_msgs in
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theorem ex4 (n : Nat) (h : n = 0) : 0 + n = 0 := by
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let m := n + 1
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let v := m + 1
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have : v = n + 2 := rfl
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subst this
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