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Proof step 10 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 ∈ vols, v0 ∈ vols, v0 ∈ vols[v, vols[v][m, unmapped]], v0 ∈ avols[v, avols[v][m, erased]], ∀ 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) ⊦ ( 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 weak cut applied rule cut formula

And obtained the following new goals

Proof step 11:
# vols[v0] = # avols[v0], apebs[vols[v, vols[v][m, unmapped]][v0][m0].pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), v0 = v, 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) ⊦ ( 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]
Proof step 15:
# 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]

Rule argument

fma: v0 = v

Additional information

Used formulas: v0 = v