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Proof step 7 from proof valid-wl-free (previous step)

apebs[m] = mkpeb(aehdr, avhdr, buf, m0, wlar[m].status = erroneous), m < # wlar, wlar[m].status = free → avhdr = empty, wlar[m].status ≠ erroneous ∧ wlar[m].status ≠ erasing → aehdr = aechdr(wlar[m].ec), wlar[m].status = used → valid-peb(v, m2, mkpeb(aehdr, avhdr, buf, m0, wlar[m].status = erroneous)) ∧ avhdr.sqn = valid-sqns(v, m2, apebs).max, ∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)), ∀ n. n < # wlar → (wlar[m, wl-entry(m1, free)][n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[m, wl-entry(m1, free)][n].status = free → apebs[n].vidhdr = empty) ∧ ( wlar[m, wl-entry(m1, free)][n].status ≠ erroneous ∧ wlar[m, wl-entry(m1, free)][n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[m, wl-entry(m1, free)][n].ec)) ∧ (wlar[m, wl-entry(m1, free)][n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)) ⊦ aehdr = aechdr(m1) ∧ avhdr = empty ∧ wlar[m].status ≠ erroneous

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
apebs[m] = mkpeb(aehdr, avhdr, buf, m0, stat = erroneous), wlar[m] = wl-entry(m3, stat), m < # wlar, stat = used → valid-peb(v, m2, mkpeb(aehdr, avhdr, buf, m0, stat = erroneous)) ∧ avhdr.sqn = valid-sqns(v, m2, apebs).max, stat ≠ erroneous ∧ stat ≠ erasing → aehdr = aechdr(m3), stat = free → avhdr = empty, ∀ n. n < # wlar → (wlar[m, wl-entry(m1, free)][n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[m, wl-entry(m1, free)][n].status = free → apebs[n].vidhdr = empty) ∧ ( wlar[m, wl-entry(m1, free)][n].status ≠ erroneous ∧ wlar[m, wl-entry(m1, free)][n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[m, wl-entry(m1, free)][n].ec)) ∧ (wlar[m, wl-entry(m1, free)][n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)), ∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)) ⊦ aehdr = aechdr(m1) ∧ avhdr = empty ∧ stat ≠ erroneous

Rule argument

spec: wlentry name: elim-02 seq: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat) subst: [wle, m, stat] → [wlar[m], m3, stat]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[m], m3, stat