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Proof step 18 from proof valid-wl-next-valid-update (previous step)

# apebs = # wlar, avhdr0.sqn = valid-sqns(v, n, apebs, m).max, apebs[m0] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), apebs[m] = mkpeb(aehdr, avhdr, buf, m3, boolvar), apebs[n0] = mkpeb(aehdr1, avhdr1, buf1, m5, boolvar1), wlar[m, wl-entry(aehdr.ec, used)][n0] = wl-entry(m6, stat), wlar[n0] = wl-entry(m7, stat0), n0 = m, m0 < # wlar, m < # wlar, avhdr0.sqn < avhdr.sqn, m0 < m, n0 < # wlar, m0 + 1 < # wlar, valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m3, boolvar)), valid-peb(v, n, mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0)), n0 ≤ m, n0 < m → (stat0 = erroneous ↔ boolvar1) ∧ (stat0 = free → avhdr1 = empty) ∧ (stat0 ≠ erroneous ∧ stat0 ≠ erasing → aehdr1 = aechdr(m7)) ∧ (stat0 = used → valid-peb(v0, m1, mkpeb(aehdr1, avhdr1, buf1, m5, false)) ∧ avhdr1.sqn = valid-sqns(v0, m1, apebs, m).max), ∀ v, m. unique-elems(valid-sqns(v, m, apebs)) ⊦ n0 = m0, (stat = erroneous ↔ boolvar1) ∧ (stat = free → avhdr1 = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr1 = aechdr(m6)) ∧ ( stat = used → (∃ v0, m2. valid-peb(v0, m2, mkpeb(aehdr1, avhdr1, buf1, m5, false)) ∧ avhdr1.sqn = (valid-sqns(v0, m2, apebs, m) ∪ (v = v0 ∧ n = m2 ⊃ {avhdr.sqn} ;∅)).max))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
# apebs = # wlar, avhdr0.sqn = valid-sqns(v, n, apebs, m).max, wlar[m] = wl-entry(m7, stat0), apebs[m0] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), apebs[m] = mkpeb(aehdr1, avhdr1, buf1, m5, false), m0 < # wlar, avhdr0.sqn < avhdr1.sqn, m0 < m, m < # wlar, m0 + 1 < # wlar, valid-peb(v, n, mkpeb(aehdr1, avhdr1, buf1, m5, false)), valid-peb(v, n, mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0)), ∀ v, m. unique-elems(valid-sqns(v, m, apebs)) ⊦ m = m0, aehdr1 = aechdr(aehdr1.ec) ∧ (∃ v0, m2. valid-peb(v0, m2, mkpeb(aechdr(aehdr1.ec), avhdr1, buf1, m5, false)) ∧ avhdr1.sqn = (valid-sqns(v0, m2, apebs, m) ∪ (v = v0 ∧ n = m2 ⊃ {avhdr1.sqn} ;∅)).max)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ used ≠ erasing; (s)% ⊦ used ≠ free; (s)% ⊦ used ≠ erroneous; (s)% ⊦ ¬ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, true)); (s)%⊦ mkpeb(aehdr, avhdr, buf, m, boolvar) = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0) ↔ aehdr = aehdr0 ∧ avhdr = avhdr0 ∧ buf = buf0 ∧ m = m0 ∧ (boolvar ↔ boolvar0); (s)% ⊦ ¬ n < n; (s)% ⊦ m ≤ m; (s)% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)% ⊦ m < # wlar → wlar[m, wle][m] = wle; (s)