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Proof step 23 from proof absexpt-pebs-write (previous step)

# vols[v0] = # avols[v0], wlar[n].status = used, apebs[n] = mkpeb(aehdr, avidhdr(v1, m4, m5, m6, m7), buf, m2, boolvar), avols[v0][m0] = mapped(buf0, m1), vols[v0][m0] = ⌜n⌝ , vols[v1][m4] = ⌜n⌝ , m4 < # vols[v1], n < # wlar, n < # apebs, m0 < # avols[v0], v0 ∈ vols, v0 ∈ avols, v1 ∈ vols, m3 ≤ m1, ∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ n0, v0 ≠ v1 ∨ m0 ≠ m4 ⊦ n = n0, buf0 = buf ∧ m2 ≤ m1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
# vols[v0] = # avols[v0], vols[v1][m4] = ⌜n⌝ , vols[v0][m0] = ⌜n⌝ , avols[v0][m0] = mapped(buf0, m1), apebs[n] = mkpeb(aehdr, avidhdr(v1, m4, m5, m6, m7), buf, m2, boolvar), wlar[n] = wl-entry(m8, stat), stat = used, m0 < # avols[v0], n < # apebs, n < # wlar, m4 < # vols[v1], v1 ∈ vols, v0 ∈ avols, v0 ∈ vols, m3 ≤ m1, ∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ n0, v0 ≠ v1 ∨ m0 ≠ m4 ⊦ n = n0, buf0 = buf ∧ m2 ≤ m1

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], m8, stat]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[n], m8, stat