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Proof step 6 from proof mapped-pebs-add-empty-vol (previous step)

⊦ (∃ v0, m. v0 ∈ vols[v, fill(mkebatbl(n), unmapped)] ∧ m < # vols[v, fill(mkebatbl(n), unmapped)][v0] ∧ vols[v, fill(mkebatbl(n), unmapped)][v0][m] = ⌜n0⌝ ) ↔ (∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n0⌝ ), v ∈ vols

User applied rule case distinction

And obtained the following new goals

Proof step 7:
∃ v0, m. v0 ∈ vols[v, fill(mkebatbl(n), unmapped)] ∧ m < # vols[v, fill(mkebatbl(n), unmapped)][v0] ∧ vols[v, fill(mkebatbl(n), unmapped)][v0][m] = ⌜n0⌝ ⊦ v ∈ vols, ∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n0⌝
Proof step 11:
∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n0⌝ ⊦ v ∈ vols, ∃ v0, m. v0 ∈ vols[v, fill(mkebatbl(n), unmapped)] ∧ m < # vols[v, fill(mkebatbl(n), unmapped)][v0] ∧ vols[v, fill(mkebatbl(n), unmapped)][v0][m] = ⌜n0⌝

Rule argument

pos: right 1

Proof step 6 from proof mapped-pebs-add-empty-vol (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information