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Proof step 8 from proof valid-wl-map-indices (previous step)

apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar), n0 < # wlar.mapIndices(nx, λ wle. wle.ec:= n), indices-erasing(wlar, nx), valid-indices(wlar, nx), valid-wl(apebs, wlar) ⊦ dups(nx), (wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0].status = erroneous ↔ boolvar) ∧ (wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0].status = free → avhdr = empty) ∧ ( wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0].status ≠ erroneous ∧ wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0].status ≠ erasing → aehdr = aechdr(wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0].ec)) ∧ ( wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0].status = used → (∃ v, m. valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0].status = erroneous)) ∧ avhdr.sqn = valid-sqns(v, m, apebs).max))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar), wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0] = wl-entry(m1, stat), n0 < # wlar.mapIndices(nx, λ wle. wle.ec:= n), indices-erasing(wlar, nx), valid-indices(wlar, nx), valid-wl(apebs, wlar) ⊦ dups(nx), (stat = erroneous ↔ boolvar) ∧ (stat = free → avhdr = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr = aechdr(m1)) ∧ (stat = used → (∃ v, m. valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, stat = erroneous)) ∧ avhdr.sqn = valid-sqns(v, m, apebs).max))

Rule argument

spec: wlentry name: elim-02 seq: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat) subst: [wle, m, stat] → [wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0], m1, stat]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar.mapIndices(nx, λ wle. wle.ec:= n)[n0], m1, stat