84 lines
1.6 KiB
Text
84 lines
1.6 KiB
Text
namespace Ex1
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variables
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(f : nat → nat → nat)
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(p : nat → nat → Prop)
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(h₁ : ∀ a b c, p b c → f a b = a)
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(x y z : nat)
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(h₂ : p y z)
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include f h₁ x y z h₂
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open tactic
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example : f x y = 0 + x :=
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begin
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rw [h₁],
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/- Resulting goals
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... ⊢ x = 0 + x
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... ⊢ p y ?m_1
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... ⊢ ℕ -- This is ?m_1
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-/
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(do n ← num_goals, guard $ n = 3),
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simp,
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exact h₂
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end
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example : f x y = 0 + x :=
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begin
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rw [h₁] {new_goals := new_goals.non_dep_only},
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/- Resulting goals
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... ⊢ x = 0 + x
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... ⊢ p y ?m_1
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?m_1 is not included as a new goal because it occurs above.
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-/
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(do n ← num_goals, guard $ n = 2),
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simp,
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exact h₂
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end
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example : f x y = 0 + x :=
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begin
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rw [h₁] {new_goals := new_goals.all},
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/- Resulting goals
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... ⊢ x = 0 + x
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... ⊢ ℕ -- This is ?m_1
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... ⊢ p y ?m_1
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The order is preserved in this mode.
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-/
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(do n ← num_goals, guard $ n = 3),
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simp,
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exact z,
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exact h₂
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end
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end Ex1
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namespace Ex2
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open tactic
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constant f : nat → nat
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constant p : nat → Prop
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/- The following lemma has an "auto_param", i.e., if `h` is not provided we
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try to synthesize it using the `assumption` tactic -/
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lemma f_lemma (a : nat) (h : p a . assumption) : f a = a :=
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sorry
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/- `rw` has support for "auto_param"'s. -/
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example (x : nat) (h : p x) : f x = 0 + x :=
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begin
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rw [f_lemma],
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(do n ← num_goals, guard $ n = 1),
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simp
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end
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/- We can disable auto_param support. -/
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example (x : nat) (h : p x) : f x = 0 + x :=
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begin
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rw [f_lemma] {auto_param := ff},
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(do n ← num_goals, guard $ n = 2),
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simp,
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exact h
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end
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end Ex2
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