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Proof step 3 from proof absexpt-avols-write (previous step)

m < # avols[v], v ∈ avols ⊦ (∀ v1. (v1 ∈ vols ↔ v1 ∈ avols[v, avols[v][m, leb]]) ∧ ( v1 ∈ vols → # vols[v1] = # avols[v, avols[v][m, leb]][v1] ∧ (∀ m1. (v1 ≠ v ∨ m1 ≠ m) ∧ m1 < # vols[v1] → (vols[v1][m1] = unmapped → ¬ avols[v, avols[v][m, leb]][v1][m1].mapped?) ∧ ( vols[v1][m1] ≠ unmapped → avols[v, avols[v][m, leb]][v1][m1].mapped? ∧ avols[v, avols[v][m, leb]][v1][m1].data = apebs[vols[v1][m1].pnum].data ∧ apebs[vols[v1][m1].pnum].fill ≤ avols[v, avols[v][m, leb]][v1][m1].fill) ∧ (avols[v, avols[v][m, leb]][v1][m1] = erased → ¬ v1 × m1 ∈ q)))) ↔ (∀ v1. (v1 ∈ vols ↔ v1 ∈ avols) ∧ ( v1 ∈ vols → # vols[v1] = # avols[v1] ∧ (∀ m1. (v1 ≠ v ∨ m1 ≠ m) ∧ m1 < # vols[v1] → (vols[v1][m1] = unmapped → ¬ avols[v1][m1].mapped?) ∧ ( vols[v1][m1] ≠ unmapped → avols[v1][m1].mapped? ∧ avols[v1][m1].data = apebs[vols[v1][m1].pnum].data ∧ apebs[vols[v1][m1].pnum].fill ≤ avols[v1][m1].fill) ∧ (avols[v1][m1] = erased → ¬ v1 × m1 ∈ q))))

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

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