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.
28 lines
1.3 KiB
Text
28 lines
1.3 KiB
Text
inductive infSeq_functor1.{u} {α : Type u} (r : α → α → Prop) (call : {α : Type u} → (r : α → α → Prop) → α → Prop) : α → Prop where
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| step : r a b → infSeq_functor1 r call b → infSeq_functor1 r call a
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def infSeq1 (r : α → α → Prop) : α → Prop := infSeq_functor1 r (infSeq1)
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coinductive_fixpoint monotonicity by sorry
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/--
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info: infSeq1.coinduct.{u_1} (pred : {α : Type u_1} → (α → α → Prop) → α → Prop)
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(hyp : ∀ {α : Type u_1} (r : α → α → Prop) (a : α), pred r a → infSeq_functor1 r (fun {α} => pred) a) {α : Type u_1}
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(r : α → α → Prop) (a✝ : α) : pred r a✝ → infSeq1 r a✝
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-/
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#guard_msgs in
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#check infSeq1.coinduct
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def infSeq_functor2 {α : Sort u} (r : α → α → Prop) (call : {α : Sort u} → (r : α → α → Prop) → α → Prop) : α → Prop := fun a =>
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∃ b, r a b ∧ call r b
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def infSeq2 (r : α → α → Prop) : α → Prop := infSeq_functor2 r infSeq2
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coinductive_fixpoint monotonicity sorry
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/--
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info: infSeq2.coinduct.{u_1} (pred : {α : Sort u_1} → (α → α → Prop) → α → Prop)
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(hyp : ∀ {α : Sort u_1} (r : α → α → Prop) (a : α), pred r a → ∃ b, r a b ∧ (fun {α} => pred) r b) {α : Sort u_1}
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(r : α → α → Prop) (a✝ : α) : pred r a✝ → infSeq2 r a✝
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-/
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#guard_msgs in
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#check infSeq2.coinduct
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