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Proof step 18 from proof valid-sqns-write-h (previous step)

apebs[m1] = mkpeb(aehdr, avhdr, buf, m0, boolvar), valid-sqns(v, m, apebs[n, apeb], m1) = (valid-sqns(v, m, apebs, m1) \ (valid-peb(v, m, apebs[n]) ⊃ {apebs[n].vidhdr.sqn} ;∅)) ∪ (valid-peb(v, m, apeb) ⊃ {apeb.vidhdr.sqn} ;∅), n + 1 < # apebs, m1 < # apebs, n < m1, n < # apebs, valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, apebs[n]) ⊦ valid-sqns(v, m, apebs[n, apeb], m1) ++ avhdr.sqn = ((valid-sqns(v, m, apebs, m1) ++ avhdr.sqn) \ {apebs[n].vidhdr.sqn} ) ∪ (valid-peb(v, m, apeb) ⊃ {apeb.vidhdr.sqn} ;∅), m1 = n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
apebs[m1] = mkpeb(aehdr, avhdr, buf, m0, boolvar), valid-sqns(v, m, apebs[n, apeb], m1) = (valid-sqns(v, m, apebs, m1) -- apebs[n].vidhdr.sqn) ∪ (valid-peb(v, m, apeb) ⊃ {apeb.vidhdr.sqn} ;∅), n < # apebs, n < m1, m1 < # apebs, n + 1 < # apebs, valid-peb(v, m, apebs[n]), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) ⊦ valid-sqns(v, m, apebs[n, apeb], m1) ++ avhdr.sqn = (avhdr.sqn = apebs[n].vidhdr.sqn ⊃ valid-sqns(v, m, apebs, m1);(valid-sqns(v, m, apebs, m1) -- apebs[n].vidhdr.sqn) ++ avhdr.sqn) ∪ (valid-peb(v, m, apeb) ⊃ {apeb.vidhdr.sqn} ;∅), m1 = n

Rule argument

Additional information

Used simplifier rules: ⊦ (bag0 ++ n) -- n0 = (n = n0 ⊃ bag0;(bag0 -- n0) ++ n); (s)% ⊦ bag \ {n} = bag -- n; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)