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Proof step 39 from proof valid-wl-write-valid (previous step)

# apebs = # wlar, stat = erroneous ↔ apebs[n].bad, apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)][n] = mkpeb(aehdr0, avhdr0, buf, m3, boolvar), wlar[m] = wl-entry(m2, used), apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), wlar[n] = wl-entry(m4, stat), m < # wlar, n < # wlar, valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), stat = used → valid-peb(v, m5, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m5, apebs).max, stat ≠ erroneous ∧ stat ≠ erasing → apebs[n].echdr = aechdr(m4), stat = free → apebs[n].vidhdr = empty ⊦ (stat = erroneous ↔ boolvar) ∧ (stat = free → avhdr0 = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr0 = aechdr(m4)) ∧ ( stat = used → (∃ v, m5. valid-peb(v, m5, mkpeb(aehdr0, avhdr0, buf, m3, false)) ∧ avhdr0.sqn = valid-sqns(v, m5, apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)]).max))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 40:
# apebs = # wlar, stat = erroneous ↔ boolvar2, wlar[n] = wl-entry(m4, stat), apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), wlar[m] = wl-entry(m2, used), apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)][n] = mkpeb(aehdr0, avhdr0, buf, m3, boolvar), apebs[n] = mkpeb(aehdr1, avhdr1, buf2, m6, boolvar2), n < # wlar, m < # wlar, valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), stat = free → avhdr1 = empty, stat ≠ erroneous ∧ stat ≠ erasing → aehdr1 = aechdr(m4), stat = used → valid-peb(v, m5, apebs[n]) ∧ avhdr1.sqn = valid-sqns(v, m5, apebs).max ⊦ (stat = erroneous ↔ boolvar) ∧ (stat = free → avhdr0 = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr0 = aechdr(m4)) ∧ ( stat = used → (∃ v, m5. valid-peb(v, m5, mkpeb(aehdr0, avhdr0, buf, m3, false)) ∧ avhdr0.sqn = valid-sqns(v, m5, apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)]).max))

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apebs[n], aehdr1, avhdr1, buf2, m6, boolvar2]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apebs[n], aehdr1, avhdr1, buf2, m6, boolvar2