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Proof step 4 from proof valid-ebatbl-add-unmapped-vol (previous step)

wlar[n1] = wl-entry(m2, free), apebs[n2] = mkpeb(aehdr, avhdr, buf, m3, boolvar), ∀ 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, fill(mkebatbl(n), unmapped)][v0][m] = ⌜n2⌝ ∧ v0 ∈ vols[v, fill(mkebatbl(n), unmapped)] ∧ m < # vols[v, fill(mkebatbl(n), unmapped)][v0] ↔ wlar[n1, wl-entry(m1, used)][n0, wl-entry(m0, erasing)][n2].status = used ∧ n2 < # apebs ∧ n2 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v0 ∧ avhdr.leb = m ∧ n2 ≠ n1, v ∈ vols

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
apebs[n2] = mkpeb(aehdr, avhdr, buf, m3, boolvar), wlar[n1] = wl-entry(m2, free), wlar[n1, wl-entry(m1, used)][n0, wl-entry(m0, erasing)][n2] = wl-entry(m4, stat), ∀ 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, fill(mkebatbl(n), unmapped)][v0][m] = ⌜n2⌝ ∧ v0 ∈ vols[v, fill(mkebatbl(n), unmapped)] ∧ m < # vols[v, fill(mkebatbl(n), unmapped)][v0] ↔ stat = used ∧ n2 < # apebs ∧ n2 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v0 ∧ avhdr.leb = m ∧ n2 ≠ n1, v ∈ vols

Rule argument

spec: wlentry name: elim-02 seq: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat) subst: [wle, m, stat] → [wlar[n1, wl-entry(m1, used)][n0, wl-entry(m0, erasing)][n2], m4, stat]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[n1, wl-entry(m1, used)][n0, wl-entry(m0, erasing)][n2], m4, stat