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Proof step 26 from proof valid-wl-next-valid-use (previous step)

# apebs = # wlar, avhdr0.sqn = valid-sqns(v0, m1, apebs, m).max, apebs[n0] = mkpeb(aechdr(m3), avhdr0, buf0, m0, false), wlar[n0] = wl-entry(m3, used), apebs[m] = mkpeb(aehdr, avhdr, buf, m2, boolvar), valid-sqns(v, n, apebs, m) = ∅, n0 + 1 < # wlar, n0 < # wlar, m < # wlar, n0 < m, valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m2, boolvar)), valid-peb(v0, m1, mkpeb(aechdr(m3), avhdr0, buf0, m0, false)) ⊦ avhdr0.sqn = (valid-sqns(v0, m1, apebs, m) ∪ (v = v0 ∧ n = m1 ⊃ {avhdr.sqn} ;∅)).max, n0 = m

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 27:
# apebs = # wlar, avhdr0.sqn = valid-sqns(v0, m1, apebs, m).max, apebs[m] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar[n0] = wl-entry(m3, used), apebs[n0] = mkpeb(aechdr(m3), avhdr0, buf0, m0, false), n = m1, v = v0, valid-sqns(v, n, apebs, m) = ∅, n0 < m, m < # wlar, n0 < # wlar, n0 + 1 < # wlar, valid-peb(v0, m1, mkpeb(aechdr(m3), avhdr0, buf0, m0, false)), valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m2, boolvar)) ⊦ avhdr0.sqn = (valid-sqns(v0, m1, apebs, m) ∪ {avhdr.sqn} ).max, n0 = m

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ ∅ ∪ bag0 = bag0; (s)%union-ass: ⊦ bag ∪ bag3 ∪ bag4 = (bag ∪ bag3) ∪ bag4; from specification bag-union[nat-bag]%union-com: ⊦ bag ∪ bag2 = bag2 ∪ bag; from specification bag-union[nat-bag]