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Proof step 20 from proof valid-wl-map-indices (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
(n0 ∈ nx ⊃ wlar[n0].ec:= n;wlar[n0]) = wl-entry(m1, stat), apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, stat0 = erroneous), wlar[n0] = wl-entry(m2, stat0), n0 < # wlar, n0 < # wlar.mapIndices(nx, λ wle. wle.ec:= n), indices-erasing(wlar, nx), valid-indices(wlar, nx), stat0 = used → valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, stat0 = erroneous)) ∧ avhdr.sqn = valid-sqns(v, m, apebs).max, stat0 ≠ erroneous ∧ stat0 ≠ erasing → aehdr = aechdr(m2), stat0 = free → avhdr = empty ⊦ dups(nx), (stat = erroneous ↔ stat0 = erroneous) ∧ (stat = free → avhdr = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr = aechdr(m1)) ∧ (stat = used → (∃ v, m. valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, false)) ∧ 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[n0], m2, stat0]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[n0], m2, stat0