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Proof step 7 from proof lf-mapped-data (previous step)

# vols[v] = # avols[v], avols[v][m] = mapped(buf1, m1), apebs[n] = mkpeb(aehdr, avhdr, buf0, m0, boolvar), vols[v][m] = ⌜n⌝ , m < # avols[v], v ∈ avols, v ∈ vols, ∀ m. m < # avols[v] → (vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ (vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = apebs[vols[v][m].pnum].data ∧ apebs[vols[v][m].pnum].fill ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q), ∀ v. (v ∈ vols ↔ v ∈ avols) ∧ ( v ∈ vols → # vols[v] = # avols[v] ∧ (∀ m. m < # vols[v] → (vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ ( vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = apebs[vols[v][m].pnum].data ∧ apebs[vols[v][m].pnum].fill ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q))) ⊦ buf1 = buf0

Heuristic quantifier applied rule all left

And closed the goal!

Rule argument

pos: left 8 terms: m

Additional information

Used simplifier rules: ⊦ erased ≠ mapped(buf, m); (s)% ⊦ unmapped ≠ ⌜m⌝ ; (s)% ⊦ mapped(buf, m).mapped?; (s)% ⊦ mapped(buf, m).data = buf; (s)% ⊦ ⌜m⌝ .pnum = m; (s)% ⊦ mapped(buf, m).fill = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s) Used terms: m