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Proof step 8 from proof vols-le-antisym (previous step)

v ∈ vols0 ↔ v ∈ vols1, ∀ 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[v] = vols1[v]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ ebatbl = ebatbl0 ↔ # ebatbl = # ebatbl0 ∧ (∀ n. n < # ebatbl → ebatbl[n] = ebatbl0[n])
Proof step 10:
v ∈ vols0 ↔ v ∈ vols1, ∀ 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])) ⊦ # vols0[v] = # vols1[v] ∧ (∀ n. n < # vols0[v] → vols0[v][n] = vols1[v][n])

Rule argument

spec: array, inst: ebatbl name: Extension seq: ⊦ ebatbl = ebatbl0 ↔ # ebatbl = # ebatbl0 ∧ (∀ n. n < # ebatbl → ebatbl[n] = ebatbl0[n]) subst: [ebatbl0, ebatbl] → [vols1[v], vols0[v]] flags: <all paths>

Additional information

Used terms: vols1[v], vols0[v]