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Proof step 15 from proof abs-erase-emptyq (previous step)

# vols[v0] = # avols[v0], apebs[vols[v, vols[v][m, unmapped]][v0][m0].pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m < # vols[v], v0 ∈ avols[v, avols[v][m, erased]], v0 ∈ vols[v, vols[v][m, unmapped]], v0 ∈ vols, v ∈ vols, v0 ∈ avols, ∀ m. m < # avols[v0] → (vols[v0][m] = unmapped → ¬ avols[v0][m].mapped?) ∧ ( vols[v0][m] ≠ unmapped → avols[v0][m].mapped? ∧ avols[v0][m].data = apebs[vols[v0][m].pnum].data ∧ apebs[vols[v0][m].pnum].fill ≤ avols[v0][m].fill) ∧ (avols[v0][m] = erased → ¬ v0 × m ∈ q) ⊦ v0 = v, ( m0 < # vols[v, vols[v][m, unmapped]][v0] → (vols[v, vols[v][m, unmapped]][v0][m0] = unmapped → ¬ avols[v, avols[v][m, erased]][v0][m0].mapped?) ∧ ( vols[v, vols[v][m, unmapped]][v0][m0] ≠ unmapped → avols[v, avols[v][m, erased]][v0][m0].mapped? ∧ avols[v, avols[v][m, erased]][v0][m0].data = buf ∧ m1 ≤ avols[v, avols[v][m, erased]][v0][m0].fill)) ∧ # vols[v, vols[v][m, unmapped]][v0] = # avols[v, avols[v][m, erased]][v0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
# vols[v0] = # avols[v0], apebs[vols[v0][m0].pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m0 < # avols[v0], m < # vols[v], v0 ∈ vols, v ∈ vols, v0 ∈ avols, ∀ m. m < # avols[v0] → (vols[v0][m] = unmapped → ¬ avols[v0][m].mapped?) ∧ ( vols[v0][m] ≠ unmapped → avols[v0][m].mapped? ∧ avols[v0][m].data = apebs[vols[v0][m].pnum].data ∧ apebs[vols[v0][m].pnum].fill ≤ avols[v0][m].fill) ∧ (avols[v0][m] = erased → ¬ v0 × m ∈ q) ⊦ v0 = v, (vols[v0][m0] = unmapped → ¬ avols[v0][m0].mapped?) ∧ (vols[v0][m0] ≠ unmapped → avols[v0][m0].mapped? ∧ avols[v0][m0].data = buf ∧ m1 ≤ avols[v0][m0].fill)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ v ≠ v0 → avols[v0, evol][v] = avols[v]; (s)% ⊦ v ≠ v0 → (v ∈ avols[v0, evol] ↔ v ∈ avols); (s)% ⊦ v ≠ v0 → (v ∈ vols[v0, ebatbl] ↔ v ∈ vols); (s)% ⊦ v ≠ v0 → vols[v0, ebatbl][v] = vols[v]; (s)