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Proof step 6 from proof in-eraseq-strong-not-valid (previous step)

avhdr.sqn = valid-sqns(v, m, apebs).max, apebs[n] = mkpeb(aehdr, avhdr, buf, m0, boolvar), m < # vols[v], valid-eraseq-strong(apebs, to-vtbl(vols), eqent + q0), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), v ∈ vols, n ∈ eqent + q0, ∀ avhdr, v, m, apebs, n, aehdr, buf, m0, boolvar, vols. ¬ ( avhdr.sqn = valid-sqns(v, m, apebs).max ∧ apebs[n] = mkpeb(aehdr, avhdr, buf, m0, boolvar) ∧ m < # vols[v] ∧ valid-eraseq-strong(apebs, to-vtbl(vols), q0) ∧ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) ∧ n ∈ q0 ∧ v ∈ vols) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
avhdr.sqn = valid-sqns(v, m, apebs).max, apebs[n] = mkpeb(aehdr, avhdr, buf, m0, boolvar), eqent.pnum < # apebs, m < # vols[v], valid-eraseq-strong(apebs, to-vtbl(vols), q0), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), v ∈ vols, n ∈ eqent ' + q0, ∀ avhdr0, v0, m1, apebs0, n0, aehdr0, buf0, m2, boolvar0, vols0. avhdr0.sqn ≠ valid-sqns(v0, m1, apebs0).max ∨ apebs0[n0] ≠ mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0) ∨ ¬ m1 < # vols0[v0] ∨ ¬ valid-eraseq-strong(apebs0, to-vtbl(vols0), q0) ∨ ¬ valid-peb(v0, m1, mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)) ∨ ¬ n0 ∈ q0 ∨ ¬ v0 ∈ vols0, ∀ v0, m1. (valid-peb(v0, m1, apebs[eqent.pnum]) ↔ eqent.lebref = v0 × m1) ∧ (eqent.lebref = v0 × m1 ∧ v0 ∈ vols ∧ m1 < # vols[v0] → apebs[eqent.pnum].vidhdr.sqn ≠ valid-sqns(v0, m1, apebs).max) ⊦ eqent.pnum ∈ q0

Rule argument

Additional information

Used simplifier rules: valid-eraseq-strong-rec: ⊦ valid-eraseq-strong(apebs, vtbl, eqent ' + q) ↔ eqent.pnum < # apebs ∧ ¬ eqent.pnum ∈ q ∧ (∀ v, m. (valid-peb(v, m, apebs[eqent.pnum]) ↔ eqent.lebref = v × m) ∧ ( eqent.lebref = v × m ∧ v ∈ vtbl ∧ m < vtbl[v] → apebs[eqent.pnum].vidhdr.sqn ≠ valid-sqns(v, m, apebs).max)) ∧ valid-eraseq-strong(apebs, vtbl, q);% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]% ⊦ v ∈ vols → to-vtbl(vols)[v] = # vols[v]; (s)% ⊦ v ∈ to-vtbl(vols) ↔ v ∈ vols; (s)% ⊦ eqent + q = eqent ' + q; (s)