e575736cae
This PR makes `fun_induction` and `fun_cases` (try to) unfold the function application of interest in the goal. The old behavior can be enabled with `set_option tactic.fun_induction.unfolding false`. For `fun_cases` this does not work yet when the function’s result type depends on one of the arguments, see issue #8296.
72 lines
1.9 KiB
Text
72 lines
1.9 KiB
Text
namespace Bug
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open Nat
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theorem div_rec_lemma {x y : Nat} : 0 < y ∧ y ≤ x → x - y < x :=
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fun ⟨ypos, ylex⟩ => sub_lt (Nat.lt_of_lt_of_le ypos ylex) ypos
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protected noncomputable def divCore (x y : Nat) (fuel : Nat) (hfuel : x < fuel): Nat :=
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match fuel with
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| 0 => by contradiction
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| succ fuel =>
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if h : 0 < y ∧ y ≤ x then
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have this := div_rec_lemma h
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Bug.divCore (x - y) y fuel (Nat.lt_of_lt_of_le (div_rec_lemma h) (Nat.le_of_lt_succ hfuel)) + 1
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else
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0
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termination_by structural fuel
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-- /--
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-- info: { funIndName := `Bug.divCore.induct,
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-- levelMask := #[],
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-- params := #[Lean.Meta.FunIndParamKind.target, Lean.Meta.FunIndParamKind.param, Lean.Meta.FunIndParamKind.target,
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-- Lean.Meta.FunIndParamKind.target] }
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-- -/
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-- #guard_msgs in
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-- run_meta
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-- let some x ← Lean.Meta.getFunIndInfo? false ``Bug.divCore | return
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-- Lean.logInfo m!"{repr x}"
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/--
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error: tactic 'fail' failed
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case case1
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x y fuel x✝ fuel✝ : Nat
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hfuel✝ : x✝ < fuel✝.succ
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h✝ : 0 < y ∧ y ≤ x✝
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this✝ : x✝ - y < x✝
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ih1✝ : Bug.divCore (x✝ - y) y fuel✝ ⋯ = 42
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⊢ Bug.divCore (x✝ - y) y fuel✝ ⋯ + 1 = 42
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case case2
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x y fuel x✝ fuel✝ : Nat
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hfuel✝ : x✝ < fuel✝.succ
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h✝ : ¬(0 < y ∧ y ≤ x✝)
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⊢ 0 = 42
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-/
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#guard_msgs(error) in
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protected theorem divCore_eq_div : Bug.divCore x y fuel h = 42 := by
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fun_induction Bug.divCore
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fail
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/--
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error: tactic 'fail' failed
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case case1
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x y fuel x✝ fuel✝ : Nat
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hfuel✝ : x✝ < fuel✝.succ
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h✝ : 0 < y ∧ y ≤ x✝
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this✝ : x✝ - y < x✝
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ih1✝ : Bug.divCore (x✝ - y) y fuel✝ ⋯ = 42
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⊢ Bug.divCore (x✝ - y) y fuel✝ ⋯ + 1 = 42
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case case2
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x y fuel x✝ fuel✝ : Nat
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hfuel✝ : x✝ < fuel✝.succ
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h✝ : ¬(0 < y ∧ y ≤ x✝)
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⊢ 0 = 42
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-/
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#guard_msgs in
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protected theorem divCore_eq_div' : Bug.divCore x y fuel h = 42 := by
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induction x, fuel, h using Bug.divCore.induct_unfolding y
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fail
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end Bug
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