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Proof step 6 from proof valid-eraseqp-update-other (previous step)

eqent = eq-entry(m0, lref), m0 < # apebs, ∀ apebs, m, apeb. (valid-eraseq(apebs[m, apeb], q0) ↔ valid-eraseq(apebs, q0)) ∨ m ∈ q0 ⊦ (valid-peb(apebs[m, apeb][m0]) → lref = apebs[m, apeb][m0].vidhdr.vol × apebs[m, apeb][m0].vidhdr.leb) ∧ valid-eraseq(apebs[m, apeb], q0) ↔ (valid-peb(apebs[m0]) → lref = apebs[m0].vidhdr.vol × apebs[m0].vidhdr.leb) ∧ valid-eraseq(apebs, q0), m ∈ eqent ', m ∈ q0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
m0 < # apebs, valid-peb(apebs[m0]) → lref = apebs[m0].vidhdr.vol × apebs[m0].vidhdr.leb, ∀ apebs, m, apeb. (valid-eraseq(apebs[m, apeb], q0) ↔ valid-eraseq(apebs, q0)) ∨ m ∈ q0 ⊦ valid-eraseq(apebs[m, apeb], q0) ↔ valid-eraseq(apebs, q0), m = m0, m ∈ q0

Rule argument

Additional information

Used simplifier rules: m ≠ n ⊦ apebs[m, apeb][n] = apebs[n]; (s)% ⊦ n ∈ eq-entry(m, lref) ' ↔ n = m; (s)% ⊦ m < # apebs → apebs[m, apeb][m] = apeb; (s)