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Proof step 35 from proof mapped-pebs-unmap (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
vols[v0][m1] = ⌜n⌝ , vols[v1][m2] = ⌜n0⌝ , apebs[n0] = mkpeb(aehdr, avidhdr(v1, m2, m3, m4, m5), buf, m6, boolvar), wlar[n0] = wl-entry(m7, used), m1 < # vols[v0], n0 < # apebs, n0 < # wlar, m2 < # vols[v1], v0 ∈ vols, v1 ∈ 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 ≠ m0 ⊦ n0 = m0, v0 = v1, n ≠ n0 ∧ (∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ )

Rule argument

Additional information

Used simplifier rules: ⊦ avidhdr(v, m, m0, m1, m2).valid?; (s)% ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ avidhdr(v, m, m0, m1, m2).vol = v; (s)% ⊦ avidhdr(v, m, m0, m1, m2).leb = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic