5c03ab9630
This PR changes the implementation of a function `unfoldPredRel` used in
(co)inductive predicate machinery, that unfolds pointwise order on
predicates to quantifications and implications. Previous implementation
relied on `withDeclsDND` that could not deal with types which depend on
each other. This caused the following example to fail:
```lean4
inductive infSeq_functor1.{u} {α : Type u} (r : α → α → Prop) (call : {α : Type u} → (r : α → α → Prop) → α → Prop) : α → Prop where
| step : r a b → infSeq_functor1 r call b → infSeq_functor1 r call a
def infSeq1 (r : α → α → Prop) : α → Prop := infSeq_functor1 r (infSeq1)
coinductive_fixpoint monotonicity by sorry
#check infSeq1.coinduct
```
Closes #10234.
122 lines
3.6 KiB
Text
122 lines
3.6 KiB
Text
namespace MutualCoinduction
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mutual
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def f : Prop :=
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g
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coinductive_fixpoint
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def g : Prop :=
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f
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coinductive_fixpoint
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end
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/--
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info: MutualCoinduction.f.coinduct (pred_1 pred_2 : Prop) (hyp_1 : pred_1 → pred_2) (hyp_2 : pred_2 → pred_1) : pred_1 → f
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-/
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#guard_msgs in
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#check MutualCoinduction.f.coinduct
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/--
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info: MutualCoinduction.f.mutual_induct (pred_1 pred_2 : Prop) (hyp_1 : pred_1 → pred_2) (hyp_2 : pred_2 → pred_1) :
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(pred_1 → f) ∧ (pred_2 → g)
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-/
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#guard_msgs in
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#check MutualCoinduction.f.mutual_induct
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/--
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info: MutualCoinduction.g.coinduct (pred_1 pred_2 : Prop) (hyp_1 : pred_1 → pred_2) (hyp_2 : pred_2 → pred_1) : pred_2 → g
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-/
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#guard_msgs in
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#check MutualCoinduction.g.coinduct
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end MutualCoinduction
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namespace MutualInduction
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mutual
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def f : Prop :=
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g
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inductive_fixpoint
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def g : Prop :=
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f
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inductive_fixpoint
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end
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/--
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info: MutualInduction.f.induct (pred_1 pred_2 : Prop) (hyp_1 : pred_2 → pred_1) (hyp_2 : pred_1 → pred_2) : f → pred_1
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-/
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#guard_msgs in
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#check MutualInduction.f.induct
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/--
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info: MutualInduction.f.mutual_induct (pred_1 pred_2 : Prop) (hyp_1 : pred_2 → pred_1) (hyp_2 : pred_1 → pred_2) :
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(f → pred_1) ∧ (g → pred_2)
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-/
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#guard_msgs in
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#check MutualInduction.f.mutual_induct
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/--
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info: MutualInduction.g.induct (pred_1 pred_2 : Prop) (hyp_1 : pred_2 → pred_1) (hyp_2 : pred_1 → pred_2) : g → pred_2
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-/
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#guard_msgs in
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#check MutualInduction.g.induct
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end MutualInduction
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namespace MixedInductionCoinduction
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mutual
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def f : Prop :=
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g → f
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inductive_fixpoint
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def g : Prop :=
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f → g
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coinductive_fixpoint
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end
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/--
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info: MixedInductionCoinduction.f.induct (pred_1 pred_2 : Prop) (hyp_1 : (pred_2 → pred_1) → pred_1)
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(hyp_2 : pred_2 → pred_1 → pred_2) : f → pred_1
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-/
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#guard_msgs in
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#check f.induct
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/--
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info: MixedInductionCoinduction.f.mutual_induct (pred_1 pred_2 : Prop) (hyp_1 : (pred_2 → pred_1) → pred_1)
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(hyp_2 : pred_2 → pred_1 → pred_2) : (f → pred_1) ∧ (pred_2 → g)
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-/
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#guard_msgs in
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#check f.mutual_induct
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/--
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info: MixedInductionCoinduction.g.coinduct (pred_1 pred_2 : Prop) (hyp_1 : (pred_2 → pred_1) → pred_1)
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(hyp_2 : pred_2 → pred_1 → pred_2) : pred_2 → g
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-/
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#guard_msgs in
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#check g.coinduct
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end MixedInductionCoinduction
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namespace DifferentPredicateTypes
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mutual
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def f (n : Nat) : Prop :=
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g (n+1) (n+2)
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coinductive_fixpoint
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def g (n m : Nat): Prop :=
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f (n + 2) ∨ g (m + 1) m
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coinductive_fixpoint
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end
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/--
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info: DifferentPredicateTypes.f.coinduct (pred_1 : Nat → Prop) (pred_2 : Nat → Nat → Prop)
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(hyp_1 : ∀ (n : Nat), pred_1 n → pred_2 (n + 1) (n + 2))
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(hyp_2 : ∀ (n m : Nat), pred_2 n m → pred_1 (n + 2) ∨ pred_2 (m + 1) m) (n : Nat) : pred_1 n → f n
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-/
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#guard_msgs in
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#check f.coinduct
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/--
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info: DifferentPredicateTypes.f.mutual_induct (pred_1 : Nat → Prop) (pred_2 : Nat → Nat → Prop)
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(hyp_1 : ∀ (n : Nat), pred_1 n → pred_2 (n + 1) (n + 2))
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(hyp_2 : ∀ (n m : Nat), pred_2 n m → pred_1 (n + 2) ∨ pred_2 (m + 1) m) :
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(∀ (n : Nat), pred_1 n → f n) ∧ ∀ (n m : Nat), pred_2 n m → g n m
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-/
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#guard_msgs in
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#check f.mutual_induct
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/--
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info: DifferentPredicateTypes.g.coinduct (pred_1 : Nat → Prop) (pred_2 : Nat → Nat → Prop)
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(hyp_1 : ∀ (n : Nat), pred_1 n → pred_2 (n + 1) (n + 2))
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(hyp_2 : ∀ (n m : Nat), pred_2 n m → pred_1 (n + 2) ∨ pred_2 (m + 1) m) (n m : Nat) : pred_2 n m → g n m
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-/
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#guard_msgs in
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#check g.coinduct
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end DifferentPredicateTypes
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