e532ce95ce
This PR changes the order of steps tried when proving equational theorems for structural recursion. In order to avoid goals that `split` cannot handle, avoid unfolding the LHS of the equation to `.brecOn` and `.rec` until after the RHS has been split into its final cases. Fixes: #10195
103 lines
3.5 KiB
Text
103 lines
3.5 KiB
Text
inductive Vec (α : Type u) : Nat → Type u
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| nil : Vec α 0
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| cons : α → {n : Nat} → Vec α n → Vec α (n+1)
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-- set_option trace.split.failure true
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-- set_option trace.split.debug true
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-- set_option trace.Elab.definition.structural.eqns true
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def decEqVecPlain {α} {a} [DecidableEq α] (x : @Vec α a) (x_1 : @Vec α a) : Decidable (x = x_1) :=
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if h : Vec.ctorIdx x = Vec.ctorIdx x_1 then
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match x, x_1, h with
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| Vec.nil, Vec.nil, _ => isTrue rfl
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| Vec.cons a_1 a_2, Vec.cons b b_1, _ =>
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if h_1 : @a_1 = @b then by
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subst h_1
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exact
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let inst := decEqVecPlain @a_2 @b_1;
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if h_2 : @a_2 = @b_1 then by subst h_2; exact isTrue rfl
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else isFalse (by intro n; injection n; apply h_2 _; assumption)
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else isFalse (by intro n_1; injection n_1; apply h_1 _; assumption)
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else isFalse (fun h' => h (congrArg Vec.ctorIdx h'))
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termination_by structural x
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-- Splitter and eqns generated just fine
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#guard_msgs(drop info) in
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#print sig decEqVecPlain.match_1
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#guard_msgs(drop info) in
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#print sig decEqVecPlain.match_1.eq_1
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/--
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info: theorem decEqVecPlain.eq_def.{u_1} : ∀ {α : Type u_1} {a : Nat} [inst : DecidableEq α] (x x_1 : Vec α a),
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decEqVecPlain x x_1 =
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if h : x.ctorIdx = x_1.ctorIdx then
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match a, x, x_1, h with
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| .(0), Vec.nil, Vec.nil, x => isTrue ⋯
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| .(n + 1), Vec.cons a_1 a_2, Vec.cons b b_1, x =>
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if h_1 : a_1 = b then
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Eq.ndrec (motive := fun b =>
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(Vec.cons a_1 a_2).ctorIdx = (Vec.cons b b_1).ctorIdx → Decidable (Vec.cons a_1 a_2 = Vec.cons b b_1))
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(fun x =>
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have inst_1 := decEqVecPlain a_2 b_1;
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if h_2 : a_2 = b_1 then
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Eq.ndrec (motive := fun b_1 =>
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(Vec.cons a_1 a_2).ctorIdx = (Vec.cons a_1 b_1).ctorIdx →
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have inst := decEqVecPlain a_2 b_1;
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Decidable (Vec.cons a_1 a_2 = Vec.cons a_1 b_1))
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(fun x =>
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have inst := decEqVecPlain a_2 a_2;
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isTrue ⋯)
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h_2 x
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else isFalse ⋯)
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h_1 x
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else isFalse ⋯
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else isFalse ⋯
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-/
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#guard_msgs(pass trace, all) in
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#print sig decEqVecPlain.eq_def
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axiom testSorry : α
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inductive I : Nat → Type u | cons : I n → I (n + 1)
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axiom P : I n → Prop
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@[instance] axiom instDecEqI : ∀ (x : I n), Decidable (P x)
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axiom R : I n → Type
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set_option trace.split.failure true in
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noncomputable def foo (x x' : I n) : R x :=
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if h : P x then
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match (generalizing := false) x, x', id h with --NB: non-FVar discr
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| .cons a_2, .cons a_2', _ => (testSorry : _ → _ → _) (foo a_2 a_2') h
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else testSorry
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termination_by structural x
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/--
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info: theorem foo.eq_def.{u_1, u_2} : ∀ {n : Nat} (x : I n) (x' : I n),
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foo x x' =
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if h : P x then
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match n, x, x', ⋯ with
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| .(n_1 + 1), a_2.cons, a_2'.cons, x_1 => testSorry (foo a_2 a_2') h
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else testSorry
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-/
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#guard_msgs(pass trace, all) in
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#print sig foo.eq_def
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noncomputable def nondep (x x' : I n) : Bool :=
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if h : P x then
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match (generalizing := false) x, x', id h with --NB: non-FVar discr
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| .cons a_2, .cons a_2', _ => nondep a_2 a_2'
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else false
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termination_by structural x
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/--
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info: theorem nondep.eq_def.{u_1, u_2} : ∀ {n : Nat} (x : I n) (x' : I n),
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nondep x x' =
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if h : P x then
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match n, x, x', ⋯ with
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| .(n + 1), a_2.cons, a_2'.cons, x => nondep a_2 a_2'
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else false
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-/
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#guard_msgs in
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#print sig nondep.eq_def
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