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Proof step 25 from proof valid-eraseq-stronger-prev-append-lref (previous step)

apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), apebs[m3] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), subarray(apebs, 0, m + 1)[m3] = mkpeb(aehdr1, avhdr1, buf1, m5, boolvar1), m3 + 1 < # apebs, m3 < m, m0 < # apebs, valid-sqns(v, n, apebs, m).max < avhdr.sqn, m0 < m, m < # apebs, m0 + 1 < # apebs, m3 < # apebs, valid-eraseq-stronger(subarray(apebs, 0, m), q0), valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-peb(v, n, apebs[m0]), 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, ∀ v0, m2. (valid-peb(v0, m2, mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0)) ↔ lref = v0 × m2) ∧ (lref = v0 × m2 → avhdr0.sqn ≠ valid-sqns(v0, m2, apebs, m).max) ⊦ m0 = m3, m3 ∈ q0, m0 ∈ q0, (valid-peb(v0, m2, mkpeb(aehdr1, avhdr1, buf1, m5, boolvar1)) ↔ lref = v0 × m2) ∧ (lref = v0 × m2 → avhdr1.sqn ≠ (valid-sqns(v0, m2, apebs, m) ∪ (v = v0 ∧ n = m2 ⊃ {avhdr.sqn} ;∅)).max) ∧ valid-eraseq-stronger(subarray(apebs, 0, m + 1), q0 + eq-entry(m0, v × n) ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
subarray(apebs, 0, m + 1)[m3] = mkpeb(aehdr1, avhdr1, buf1, m5, boolvar1), apebs[m3] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m3 < # apebs, m0 + 1 < # apebs, m < # apebs, m0 < m, valid-sqns(v, n, apebs, m).max < avhdr.sqn, m0 < # apebs, m3 < m, m3 + 1 < # apebs, valid-eraseq-stronger(subarray(apebs, 0, m), q0), valid-eraseq-stronger(subarray(apebs, 0, m + 1), q0 + eq-entry(m0, v × n) '), valid-peb(v, n, apebs[m0]), valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m1, boolvar)), ∀ v0, m2. (valid-peb(v0, m2, mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0)) ↔ lref = v0 × m2) ∧ (lref = v0 × m2 → avhdr0.sqn ≠ valid-sqns(v0, m2, apebs, m).max) ⊦ m0 = m3, m0 ∈ q0, m3 ∈ q0, (valid-peb(v0, m2, mkpeb(aehdr1, avhdr1, buf1, m5, boolvar1)) ↔ lref = v0 × m2) ∧ (lref = v0 × m2 → avhdr1.sqn ≠ (valid-sqns(v0, m2, apebs, m) ∪ (v = v0 ∧ n = m2 ⊃ {avhdr.sqn} ;∅)).max)

Rule argument

Additional information

Used simplifier rules: ⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)