Idris htSubst COMPLETE (all 15 cases) + substLemma0 — substitution layer of #108#119
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…s (toward #108) The QTT substitution lemma htSubst is now fully proved (all 15 cases, total, hole-free) on the Idris track, mirroring Coq ht_subst. The 5 usage-splitting cases land via the accounting algebra: - Tensor / LetPair / Case : usplit3 (USnoc-boundary split) x2 -> uaddSplitBoundary2 -> recurse -> substReassocMult -> uaddUappend - App / Let : the q-scaled variants via substReassocAdd + uscaleUappend (Let also needs uaddComm/qAddComm for the d1-scaled shape) - binder cases (LetPair/Case/Let) recurse with the prefix I extended and the body usage reshaped (USnoc..); Case unifies the two branch residuals (justInj' on the shared d2 split). Build green 8/8; the ONLY remaining hole in the whole solo-core is ?todo_preservation. Next: substLemma0 + subst2Lemma (corollaries) then the Step-induction closes preservation.
…ward #108) substLemma0 = htSubst at the empty prefix (I = TEmpty): substitute the single top-of-context variable once, the workhorse the reduction rules S_App / S_CaseL / S_CaseR / S_Let consume. One-liner over the now-complete htSubst; build green. Layer 4c (the QTT substitution lemma) is now: htSubst COMPLETE (15/15) + substLemma0. Remaining for preservation (4d): uaddAssoc -> subst2Lemma (the two-variable LetPair substitution), then the Step-induction.
… (Idris #108) Idris preservation row: foundation -> htSubst COMPLETE (15/15, b-erasure resolved) + substLemma0; only ?todo_preservation remains; subst2Lemma (via uaddAssoc) + the Step-induction are the documented remainder.
hyperpolymath
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June 20, 2026 14:02
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Summary
Completes the QTT substitution lemma
htSubston the Idris track and lands itssubst0corollary — the substitution layer (4c) ofpreservation(#108).htSubstCOMPLETE (all 15 cases, total, hole-free)The 5 usage-splitting cases are filled, so
htSubst(mirror of Coqht_subst) is fully proved:usplit3(USnoc-boundary split) ×2 →uaddSplitBoundary2→ recurse →substReassocMult→uaddUappend.q-scaled variants viasubstReassocAdd+uscaleUappend(Let also needsuaddComm/qAddCommfor thed1-scaled accounting).Iextended and body usage reshaped; Case unifies its two branch residuals (justInj'on the sharedd2split).The
b-index-erasure obstruction (ADR-003) that stalled this is resolved by carryingbas an erased implicit in bothhvSubstandhtSubst.substLemma0The
subst0corollary =htSubstat the empty prefixI = TEmpty— the workhorseS_App/S_CaseL/S_CaseR/S_Letwill consume.Registry
proofs/STATUS.mdupdated: the Idrispreservationrow now recordshtSubstCOMPLETE +substLemma0; the only remaining hole in the whole solo-core is?todo_preservation.Remaining for
preservation(4d, next)uaddAssoc→subst2Lemma(two-variableLetPairsubstitution) → theStep-induction.preservationis still NOT proved (honest).Test plan
idris2 --build solo-core.ipkgexits 0 (8/8); only?todo_preservationopen%default total, no postulatesRefs #108,
proofs/STATUS.md🤖 Generated with Claude Code
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