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Proof step 11 from proof valid-wl-next-invalid-erase (previous step)

# apebs = # wlar, apebs[m] = mkpeb(aehdr, avhdr, buf, m2, false), apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar), n < # wlar, m < # wlar, n ≤ m, ∀ n. n < m → (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, m1. valid-peb(v, m1, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m1, apebs, m).max)) ⊦ valid-peb(mkpeb(aehdr, avhdr, buf, m2, false)), (wlar[m, wl-entry(m0, erasing)][n].status = erroneous ↔ boolvar) ∧ (wlar[m, wl-entry(m0, erasing)][n].status = free → avhdr0 = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[m, wl-entry(m0, erasing)][n].status ≠ erasing → aehdr0 = aechdr(wlar[n].ec)) ∧ ( wlar[m, wl-entry(m0, erasing)][n].status = used → (∃ v, m1. valid-peb(v, m1, mkpeb(aehdr0, avhdr0, buf0, m3, wlar[n].status = erroneous)) ∧ avhdr0.sqn = valid-sqns(v, m1, apebs, m).max))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
# apebs = # wlar, apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar), apebs[m] = mkpeb(aehdr, avhdr, buf, m2, false), wlar[n] = wl-entry(m4, stat), m < # wlar, n < # wlar, n ≤ m, ∀ n. n < m → (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, m1. valid-peb(v, m1, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m1, apebs, m).max)) ⊦ valid-peb(mkpeb(aehdr, avhdr, buf, m2, false)), (wlar[m, wl-entry(m0, erasing)][n].status = erroneous ↔ boolvar) ∧ (wlar[m, wl-entry(m0, erasing)][n].status = free → avhdr0 = empty) ∧ (stat ≠ erroneous ∧ wlar[m, wl-entry(m0, erasing)][n].status ≠ erasing → aehdr0 = aechdr(m4)) ∧ ( wlar[m, wl-entry(m0, erasing)][n].status = used → (∃ v, m1. valid-peb(v, m1, mkpeb(aehdr0, avhdr0, buf0, m3, stat = erroneous)) ∧ avhdr0.sqn = valid-sqns(v, m1, apebs, m).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[n], m4, stat]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[n], m4, stat