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Proof step 3 from proof vols-le-antisym (previous step)

∀ v. (v ∈ vols1 ↔ v ∈ vols0) ∧ (v ∈ vols1 → # vols1[v] = # vols0[v] ∧ (∀ m. m < # vols1[v] ∧ vols1[v][m] ≠ unmapped → vols1[v][m] = vols0[v][m])), ∀ v. (v ∈ vols0 ↔ v ∈ vols1) ∧ (v ∈ vols0 → # vols0[v] = # vols1[v] ∧ (∀ m. m < # vols0[v] ∧ vols0[v][m] ≠ unmapped → vols0[v][m] = vols1[v][m])) ⊦ vols0 = vols1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ vols = vols0 ↔ (∀ v. (v ∈ vols ↔ v ∈ vols0) ∧ vols[v] = vols0[v])
Proof step 5:
∀ v. (v ∈ vols0 ↔ v ∈ vols1) ∧ (v ∈ vols0 → # vols0[v] = # vols1[v] ∧ (∀ m. m < # vols0[v] ∧ vols0[v][m] ≠ unmapped → vols0[v][m] = vols1[v][m])), ∀ v. (v ∈ vols1 ↔ v ∈ vols0) ∧ (v ∈ vols1 → # vols1[v] = # vols0[v] ∧ (∀ m. m < # vols1[v] ∧ vols1[v][m] ≠ unmapped → vols1[v][m] = vols0[v][m])) ⊦ ∀ v. (v ∈ vols0 ↔ v ∈ vols1) ∧ vols0[v] = vols1[v]

Rule argument

spec: store, inst: volumes name: Extension seq: ⊦ vols = vols0 ↔ (∀ v. (v ∈ vols ↔ v ∈ vols0) ∧ vols[v] = vols0[v]) subst: [vols0, vols] → [vols1, vols0] flags: <all paths>

Additional information

Used terms: vols1, vols0