[Imprint][Data Privacy Statement][E-Mail]

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Proof step 5 from proof absexpt-idset (previous step)

v0 ∈ vols ↔ v0 ∈ avols, apebs1[vols[v0][m0].pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), vols[v][m] = ⌜n⌝ , m < # vols[v], id(apebs1, apebs0, mapped-pebs(vols) -- n), valid-ebatbl(apebs0, wlar, vols, n0), v ∈ vols, v0 ∈ vols → # vols[v0] = # avols[v0] ∧ (∀ m. m < # vols[v0] → (vols[v0][m] = unmapped → ¬ avols[v0][m].mapped?) ∧ ( vols[v0][m] ≠ unmapped → avols[v0][m].mapped? ∧ avols[v0][m].data = apebs0[vols[v0][m].pnum].data ∧ apebs0[vols[v0][m].pnum].fill ≤ avols[v0][m].fill) ∧ (avols[v0][m] = erased → ¬ v0 × m ∈ q)) ⊦ (v0 ∈ vols ↔ v0 ∈ avols) ∧ ( v0 ∈ vols → # vols[v0] = # avols[v0] ∧ ( (v0 ≠ v ∨ m0 ≠ m) ∧ m0 < # vols[v0] → (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) ∧ (avols[v0][m0] = erased → ¬ v0 × m0 ∈ q)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
# vols[v0] = # avols[v0], apebs1[vols[v0][m0].pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), vols[v][m] = ⌜n⌝ , m0 < # avols[v0], m < # vols[v], id(apebs1, apebs0, mapped-pebs(vols) -- n), valid-ebatbl(apebs0, wlar, vols, n0), v0 ∈ avols, v0 ∈ vols, v ∈ 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 = apebs0[vols[v0][m].pnum].data ∧ apebs0[vols[v0][m].pnum].fill ≤ avols[v0][m].fill) ∧ (avols[v0][m] = erased → ¬ v0 × m ∈ q), v0 ≠ v ∨ m0 ≠ m ⊦ (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) ∧ (avols[v0][m0] = erased → ¬ v0 × m0 ∈ 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