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Proof step 4 from proof valid-eraseqp-update-other (previous step)

∀ apebs, m, apeb. (valid-eraseq(apebs[m, apeb], q0) ↔ valid-eraseq(apebs, q0)) ∨ m ∈ q0 ⊦ valid-eraseq(apebs[m, apeb], eqent + q0) ↔ valid-eraseq(apebs, eqent + q0), m ∈ eqent + q0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
eqent.pnum < # apebs, ∀ apebs, m, apeb. (valid-eraseq(apebs[m, apeb], q0) ↔ valid-eraseq(apebs, q0)) ∨ m ∈ q0 ⊦ (valid-peb(apebs[m, apeb][eqent.pnum]) → eqent.lebref = apebs[m, apeb][eqent.pnum].vidhdr.vol × apebs[m, apeb][eqent.pnum].vidhdr.leb) ∧ valid-eraseq(apebs[m, apeb], q0) ↔ (valid-peb(apebs[eqent.pnum]) → eqent.lebref = apebs[eqent.pnum].vidhdr.vol × apebs[eqent.pnum].vidhdr.leb) ∧ valid-eraseq(apebs, q0), m ∈ q0, m ∈ eqent '

Rule argument

Additional information

Used simplifier rules: valid-eraseqp-rec: ⊦ valid-eraseq(apebs, eqent ' + q) ↔ eqent.pnum < # apebs ∧ ( valid-peb(apebs[eqent.pnum]) → eqent.lebref = apebs[eqent.pnum].vidhdr.vol × apebs[eqent.pnum].vidhdr.leb) ∧ valid-eraseq(apebs, q);% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ n ∈ q0 + q1 ↔ n ∈ q0 ∨ n ∈ q1; (ss)%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]% ⊦ # apebs[n, apeb] = # apebs; (s)% ⊦ eqent + q = eqent ' + q; (s)