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Proof step 3 from proof valid-ebatbl-unmap (previous step)

vols[v][m] = ⌜n⌝ , m < # vols[v], v ∈ vols, ∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0 ⊦ vols[v, vols[v][m, unmapped]][v0][m1] = ⌜n1⌝ ∧ v0 ∈ vols[v, vols[v][m, unmapped]] ∧ m1 < # vols[v, vols[v][m, unmapped]][v0] ↔ wlar[n, wl-entry(m0, erasing)][n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v0 ∧ apebs[n1].vidhdr.leb = m1 ∧ n1 ≠ n0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
vols[v][m] = ⌜n⌝ , wlar[n, wl-entry(m0, erasing)][n1] = wl-entry(m2, stat), m < # vols[v], v ∈ vols, ∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0 ⊦ vols[v, vols[v][m, unmapped]][v0][m1] = ⌜n1⌝ ∧ v0 ∈ vols[v, vols[v][m, unmapped]] ∧ m1 < # vols[v, vols[v][m, unmapped]][v0] ↔ stat = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v0 ∧ apebs[n1].vidhdr.leb = m1 ∧ n1 ≠ n0

Rule argument

spec: wlentry name: elim-02 seq: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat) subst: [wle, m, stat] → [wlar[n, wl-entry(m0, erasing)][n1], m2, stat]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[n, wl-entry(m0, erasing)][n1], m2, stat