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Proof step 5 from proof valid-eraseq-stronger-prev-append-lref (previous step)

apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m0 + 1 < # apebs, m < # apebs, m0 < m, valid-sqns(v, n, apebs, m).max < avhdr.sqn, m0 < # apebs, valid-eraseq-stronger(subarray(apebs, 0, m), q), valid-peb(v, n, apebs[m0]), valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊦ valid-eraseq-stronger(subarray(apebs, 0, m + 1), q + eq-entry(m0, v × n) '), m0 ∈ q

User applied rule structural induction

And obtained the following new goals

Proof step 6:
apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m0 < # apebs, valid-sqns(v, n, apebs, m).max < avhdr.sqn, m0 < m, m < # apebs, m0 + 1 < # apebs, valid-eraseq-stronger(subarray(apebs, 0, m), []), valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-peb(v, n, apebs[m0]) ⊦ valid-eraseq-stronger(subarray(apebs, 0, m + 1), [] + eq-entry(m0, v × n) '), m0 ∈ []
Proof step 17:
apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m0 < # apebs, valid-sqns(v, n, apebs, m).max < avhdr.sqn, m0 < m, m < # apebs, m0 + 1 < # apebs, valid-eraseq-stronger(subarray(apebs, 0, m), eqent + q0), valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-peb(v, n, apebs[m0]), ∀ apebs, m, aehdr, avhdr, buf, m1, boolvar, m0, v, n. apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar) ∧ m0 + 1 < # apebs ∧ m < # apebs ∧ m0 < m ∧ valid-sqns(v, n, apebs, m).max < avhdr.sqn ∧ m0 < # apebs ∧ valid-eraseq-stronger(subarray(apebs, 0, m), q0) ∧ valid-peb(v, n, apebs[m0]) ∧ valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m1, boolvar)) → valid-eraseq-stronger(subarray(apebs, 0, m + 1), q0 + eq-entry(m0, v × n) ') ∨ m0 ∈ q0 ⊦ valid-eraseq-stronger(subarray(apebs, 0, m + 1), (eqent + q0) + eq-entry(m0, v × n) '), m0 ∈ eqent + q0

Rule argument

indvar: q

Additional information

Used simplifier rules: queue freely generated by [], +;;