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Proof step 47 from proof valid-wl-write-valid (previous step)

# apebs = # wlar, apebs[n] = mkpeb(aehdr1, avhdr1, buf2, m6, stat = erroneous), 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, mkpeb(aehdr1, avhdr1, buf2, m6, false)) ∧ avhdr1.sqn = valid-sqns(v, m5, apebs).max, stat ≠ erroneous ∧ stat ≠ erasing → aehdr1 = aechdr(m4), stat = free → avhdr1 = empty ⊦ n = m, (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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
# apebs = # wlar, avhdr1.sqn = valid-sqns(v, m5, apebs).max, apebs[n] = mkpeb(aechdr(m4), avhdr1, buf2, m6, false), wlar[n] = wl-entry(m4, used), apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), wlar[m] = wl-entry(m2, used), n < # wlar, m < # wlar, valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), valid-peb(v, m5, mkpeb(aechdr(m4), avhdr1, buf2, m6, false)) ⊦ avhdr1.sqn = valid-sqns(v, m5, apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)]).max, n = m

Rule argument

Additional information

Used simplifier rules: ⊦ used ≠ erasing; (s)% ⊦ used ≠ erroneous; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)% ⊦ used ≠ free; (s)%⊦ mkpeb(aehdr, avhdr, buf, m, boolvar) = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0) ↔ aehdr = aehdr0 ∧ avhdr = avhdr0 ∧ buf = buf0 ∧ m = m0 ∧ (boolvar ↔ boolvar0); (s)% ⊦ m ≠ n → apebs[n, apeb][m] = apebs[m]; (s)