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Proof step 11 from proof abs-unmap (previous step)

# vols[v0] = # avols[v0], v0 ∈ vols ↔ v0 ∈ avols, apebs[vols[v0][m0].pnum] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), apebs[vols[v, vols[v][m, unmapped]][v0][m0].pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), vols[v][m] = ⌜n⌝ , v0 = v, m < # vols[v], v ∈ vols, m0 < # avols[v0] → (vols[v0][m0] = unmapped → ¬ avols[v0][m0].mapped?) ∧ (vols[v0][m0] ≠ unmapped → avols[v0][m0].mapped? ∧ avols[v0][m0].data = buf0 ∧ m2 ≤ avols[v0][m0].fill) ∧ (avols[v0][m0] = erased → ¬ v0 × m0 ∈ q) ⊦ (v0 ∈ vols[v, vols[v][m, unmapped]] ↔ v0 ∈ avols[v, avols[v][m, unmapped]]) ∧ ( v0 ∈ vols[v, vols[v][m, unmapped]] → # vols[v, vols[v][m, unmapped]][v0] = # avols[v, avols[v][m, unmapped]][v0] ∧ ( m0 < # vols[v, vols[v][m, unmapped]][v0] → (vols[v, vols[v][m, unmapped]][v0][m0] = unmapped → ¬ avols[v, avols[v][m, unmapped]][v0][m0].mapped?) ∧ ( vols[v, vols[v][m, unmapped]][v0][m0] ≠ unmapped → avols[v, avols[v][m, unmapped]][v0][m0].mapped? ∧ avols[v, avols[v][m, unmapped]][v0][m0].data = buf ∧ m1 ≤ avols[v, avols[v][m, unmapped]][v0][m0].fill) ∧ (avols[v, avols[v][m, unmapped]][v0][m0] = erased → ¬ v0 × m0 ∈ q + eq-entry(n, v × m) ')))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# vols[v] = # avols[v], apebs[vols[v][m0].pnum] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), apebs[vols[v][m, unmapped][m0].pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), vols[v][m] = ⌜n⌝ , m0 < # avols[v], m < # avols[v], v ∈ avols, v ∈ vols, vols[v][m0] = unmapped → ¬ avols[v][m0].mapped?, vols[v][m0] ≠ unmapped → avols[v][m0].mapped? ∧ avols[v][m0].data = buf0 ∧ m2 ≤ avols[v][m0].fill, avols[v][m0] = erased → ¬ v × m0 ∈ q ⊦ (vols[v][m0] = unmapped → ¬ avols[v][m, unmapped][m0].mapped?) ∧ (vols[v][m, unmapped][m0] ≠ unmapped → avols[v][m0].mapped? ∧ avols[v][m0].data = buf ∧ m1 ≤ avols[v][m0].fill) ∧ (avols[v][m, unmapped][m0] = erased → ¬ v × m0 ∈ q + eq-entry(n, v × m) ')

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%m ≠ n ⊦ evol[m, leb][n] = evol[n]; (s)%m ≠ n ⊦ ebatbl[m, ebae][n] = ebatbl[n]; (s)% ⊦ ¬ unmapped.mapped?; (s)% ⊦ m < # evol → evol[m, leb][m] = leb; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < # ebatbl → ebatbl[m, ebae][m] = ebae; (s)% ⊦ # evol[n, leb] = # evol; (s)% ⊦ avols[v, evol][v] = evol; (s)% ⊦ # ebatbl[n, ebae] = # ebatbl; (s)% ⊦ v ∈ avols[v, evol]; (s)% ⊦ v ∈ vols[v, ebatbl]; (s)% ⊦ vols[v, ebatbl][v] = ebatbl; (s)