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Proof step 11 from proof absexpt-v-vols-write (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# vols[v0] = # avols[v0], # evol = # ebatbl, apebs[vols[v0][m].pnum] = mkpeb(aehdr, avhdr, buf, m0, boolvar), m < # avols[v0], v0 ∈ avols, v0 ∈ vols, ∀ 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) ⊦ v ∈ vols, v ∈ avols, (vols[v0][m] = unmapped → ¬ avols[v0][m].mapped?) ∧ (vols[v0][m] ≠ unmapped → avols[v0][m].mapped? ∧ avols[v0][m].data = buf ∧ m0 ≤ avols[v0][m].fill) ∧ (avols[v0][m] = erased → ¬ v0 × m ∈ q)

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 ∈ avols ∧ ¬ v0 ∈ avols → avols[v0, evol][v] = avols[v]; (s)% ⊦ v ≠ v0 → vols[v0, ebatbl][v] = vols[v]; (s)% ⊦ v ≠ v0 → (v ∈ avols[v0, evol] ↔ v ∈ avols); (s)% ⊦ v ≠ v0 → (v ∈ vols[v0, ebatbl] ↔ v ∈ vols); (s)