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

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

User applied rule structural induction

And obtained the following new goals

Proof step 6:
apebs[m] = mkpeb(aehdr, avhdr, buf, m0, boolvar), m < # apebs, valid-eraseq-stronger(subarray(apebs, 0, m), []) ⊦ valid-eraseq-stronger(subarray(apebs, 0, m + 1), [] + eq-entry(m, v × n) ') ↔ valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m0, boolvar)) ∧ valid-sqns(v, n, apebs, m) ≠ ∅ ∧ avhdr.sqn < valid-sqns(v, n, apebs, m).max
Proof step 11:
apebs[m] = mkpeb(aehdr, avhdr, buf, m0, boolvar), m < # apebs, valid-eraseq-stronger(subarray(apebs, 0, m), eqent + q0), ∀ apebs, m, aehdr, avhdr, buf, m0, boolvar, v, n. apebs[m] = mkpeb(aehdr, avhdr, buf, m0, boolvar) ∧ m < # apebs ∧ valid-eraseq-stronger(subarray(apebs, 0, m), q0) → ( valid-eraseq-stronger(subarray(apebs, 0, m + 1), q0 + eq-entry(m, v × n) ') ↔ valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m0, boolvar)) ∧ valid-sqns(v, n, apebs, m) ≠ ∅ ∧ avhdr.sqn < valid-sqns(v, n, apebs, m).max) ⊦ valid-eraseq-stronger(subarray(apebs, 0, m + 1), (eqent + q0) + eq-entry(m, v × n) ') ↔ valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m0, boolvar)) ∧ valid-sqns(v, n, apebs, m) ≠ ∅ ∧ avhdr.sqn < valid-sqns(v, n, apebs, m).max

Rule argument

indvar: q

Additional information

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