feat(Order/OmegaCompletePartialOrder): least fixed point and Scott induction#38316
feat(Order/OmegaCompletePartialOrder): least fixed point and Scott induction#38316tannerduve wants to merge 2 commits intoleanprover-community:masterfrom
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PR summary 98261a9c88Import changes for modified filesNo significant changes to the import graph Import changes for all files
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…duction Add `lfp` for ω-Scott continuous endofunctions on an ωCPO with `⊥`, defined as the supremum of the iteration chain from `⊥`, together with its basic API (`map_lfp`, `isFixedPt_lfp`, `lfp_le_fixed`, `isLeast_lfp`) and a Scott induction principle `lfp_induction`. Also add corresponding induction principles for `Part.fix`: `fix_scott_induction` (ω-Scott continuous functional, admissible predicate) and `fix_scott_induction_pointwise` (no continuity hypothesis, conclusion of the form `Part.fix g x = some y → P x y`), supported by a helper `exists_approx_eq_of_fix_eq_some`.
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…ction Add `fix_eq_lfp` identifying `Part.fix g` with `ContinuousHom.lfp` of the associated continuous map, and reduce `fix_scott_induction` to a direct application of `ContinuousHom.lfp_induction`.
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lfpfor endomorphisms on an ωCPO with a least element and its basic API (map_lfp,isFixedPt_lfp,lfp_le_fixed,isLeast_lfp) and the Scott induction theoremlfp_inductionAlso add corresponding induction principles for
Part.fix:fix_scott_induction(ω-Scott continuous functional, admissible predicate) andfix_scott_induction_pointwise