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@thomaskwaring Sorry for the wait. Could you please take a look at this PR? |
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…quivalences Introduce intermediate commutation notions between single-step and multi-step properties: - TransGenCommute: single r₁ + single r₂ join via TransGen r₂ and ReflTransGen r₁ - SemiDiamondCommute: single r₁ + TransGen r₂ join via TransGen r₂ and ReflTransGen r₁ Prove the corresponding implications and equivalences mirroring the existing SemiCommute ↔ Commute development, including: - SemiDiamondCommute ↔ DiamondCommute (ReflTransGen r₁) (TransGen r₂) - Commute ∧ TransGenCommute ↔ SemiDiamondCommute
5 version of eta-postpone theorems:
* `transgen_postpone_eta_beta`: if `P →ηᶠ Q` and `Q →βᶠ R`, then there is a term
`S` with `P ↠β+ S` and `S ↠ηᶠ R`.
* `commute_etastar_beta`: if `P ↠ηᶠ Q` and `Q ↠βᶠ R`, then there is a term
`S` with `P ↠βᶠ S` and `S ↠ηᶠ R`.
* `semiDiamondCommute_eta_beta`: if `P →ηᶠ Q` and `Q ↠β+ R`, then there is a term
`S` with `P ↠β+ S` and `S ↠ηᶠ R`.
* `diamondcommute_etaplus_betastar`: if `P ↠ηᶠ Q` and `Q ↠β+ R`, then there is
a term `S` with `P ↠β+ S` and `S ↠ηᶠ R`.
* `eta_postpone`: if `P ↠βηᶠ Q`, then there is a term `S` such that
`P ↠βᶠ S` and `S ↠ηᶠ Q`.
Ai usage:
`ParEta.lean` and `BetaNfLc.lean` are generated by @Aristotle-Harmonic
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5 version of eta-postpone theorems:
transgen_postpone_eta_beta: ifP →ηᶠ QandQ →βᶠ R, then there is a termSwithP ↠β+ SandS ↠ηᶠ R.commute_etastar_beta: ifP ↠ηᶠ QandQ ↠βᶠ R, then there is a termSwithP ↠βᶠ SandS ↠ηᶠ R.semiDiamondCommute_eta_beta: ifP →ηᶠ QandQ ↠β+ R, then there is a termSwithP ↠β+ SandS ↠ηᶠ R.diamondcommute_etaplus_betastar: ifP ↠ηᶠ QandQ ↠β+ R, then there isa term
SwithP ↠β+ SandS ↠ηᶠ R.eta_postpone: ifP ↠βηᶠ Q, then there is a termSsuch thatP ↠βᶠ SandS ↠ηᶠ Q.Ai usage:
ParEta.leanandBetaNfLc.leanare generated by @Aristotle-Harmonic