d60ef53d54
This PR changes `Lean.Order.CCPO` and `.CompleteLattice` to carry a Prop. This avoids the `CCPO IO` instance from being `noncomputable`.
57 lines
1.8 KiB
Text
57 lines
1.8 KiB
Text
set_option warn.sorry false
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axiom A : Type
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axiom B : Type
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axiom A.toB : A → B
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axiom B.toA : B → A
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open Lean.Order
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instance : PartialOrder A := sorry
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-- It’s important that the CCPO instance isn't completely axiomatic, so that
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-- `instCCPO.toOrder` is defeq to `instOrder`
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instance : CCPO A where
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has_csup := sorry
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instance : PartialOrder B := sorry
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instance : CCPO B where
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has_csup := sorry
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@[partial_fixpoint_monotone] axiom monotone_toA :
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∀ {α} [PartialOrder α] (f : α → B), monotone f → monotone (fun x => B.toA (f x))
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@[partial_fixpoint_monotone] axiom monotone_toB :
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∀ {α} [PartialOrder α] (f : α → A), monotone f → monotone (fun x => A.toB (f x))
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mutual
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noncomputable def f : A := g.toA
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partial_fixpoint
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noncomputable def g : B := f.toB
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partial_fixpoint
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end
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/--
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info: equations:
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theorem f.eq_1 : f = g.toA
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-/
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#guard_msgs in #print equations f
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/--
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info: f.fixpoint_induct (motive_1 : A → Prop) (motive_2 : B → Prop) (adm_1 : admissible motive_1)
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(adm_2 : admissible motive_2) (h_1 : ∀ (g : B), motive_2 g → motive_1 g.toA)
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(h_2 : ∀ (f : A), motive_1 f → motive_2 f.toB) : motive_1 f
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-/
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#guard_msgs in
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#check f.fixpoint_induct
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/--
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info: g.fixpoint_induct (motive_1 : A → Prop) (motive_2 : B → Prop) (adm_1 : admissible motive_1)
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(adm_2 : admissible motive_2) (h_1 : ∀ (g : B), motive_2 g → motive_1 g.toA)
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(h_2 : ∀ (f : A), motive_1 f → motive_2 f.toB) : motive_2 g
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-/
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#guard_msgs in
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#check g.fixpoint_induct
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/--
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info: f.mutual_fixpoint_induct (motive_1 : A → Prop) (motive_2 : B → Prop) (adm_1 : admissible motive_1)
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(adm_2 : admissible motive_2) (h_1 : ∀ (g : B), motive_2 g → motive_1 g.toA)
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(h_2 : ∀ (f : A), motive_1 f → motive_2 f.toB) : motive_1 f ∧ motive_2 g
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-/
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#guard_msgs in
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#check f.mutual_fixpoint_induct
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