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Proof step 2 from proof valid-eraseq-prev-erasing (previous step)

m1 < m, m < # wlar, valid-eraseq(subarray(wlar, 0, m), q) ⊦ valid-eraseq(subarray(wlar[m, wl-entry(m0, used)][m1, wl-entry(m2, erasing)], 0, m + 1), q + eq-entry(m1, lref) ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
m1 < # wlar, m1 < m, m < # wlar, m1 + 1 < # wlar, ∀ n. n ∈ q ↔ n < m ∧ wlar[n].status = erasing ⊦ n ∈ q + eq-entry(m1, lref) ' ↔ ¬ m < n ∧ wlar[m, wl-entry(m0, used)][m1, wl-entry(m2, erasing)][n].status = erasing

Rule argument

Additional information

Used simplifier rules: valid-eraseqw: ⊦ valid-eraseq(wlar, q) ↔ (∀ n. n ∈ q ↔ n < # wlar ∧ wlar[n].status = erasing);%ls-at-subarray-wlar: n0 ≤ # wlar, n1 < n0 ⊦ subarray(wlar, 0, n0)[n1] = wlar[n1];% ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ # wlar[n, wle] = # wlar; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m < n → m ≤ n; (s)% ⊦ # subarray(wlar, m, n) = n; (s)