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Proof step 16 from proof abs-lebrefs-subset-noterased-some (previous step)

# vols[v0] = # avols[v0], # vols[v] = # avols[v], avols[v0][m0] = erased, apebs[unmapped.pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), vols[v0][m0] = unmapped, apebs[vols[v][m].pnum] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), m0 < # avols[v0], m < # avols[v], v0 × m0 ∈ q1, v0 ∈ avols, v0 ∈ vols, v ∈ avols, v ∈ vols, vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = buf0 ∧ m2 ≤ avols[v][m].fill, vols[v][m] = unmapped → ¬ avols[v][m].mapped?, ∀ 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 ∈ q0), ∀ 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 ∈ q0))), ∀ 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 ∈ q0), ∀ lref. lref ∈ q1 ∧ lref ≠ none → lref = v × m ∨ lref ∈ q0 ⊦ avols[v][m] = erased, v0 × m0 ∈ q0

Heuristic quantifier applied rule all left

And closed the goal!

Rule argument

pos: left 19 terms: v0 × m0

Additional information

Used simplifier rules: ⊦ none ≠ v × m; (s)% ⊦ v × m = v0 × m0 ↔ v = v0 ∧ m = m0; (ws) Used terms: v0 × m0