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Proof step 2 from proof abs-nobuffer (previous step)

# avol0 = # avol1, ∀ n. n < # avol1 → avol0[n] = avol1[n] ⊦ avol0 = avol1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ avol = avol0 ↔ # avol = # avol0 ∧ (∀ n. n < # avol → avol[n] = avol0[n])
Proof step 4:
# avol0 = # avol1, ∀ n. n < # avol1 → avol0[n] = avol1[n] ⊦ # avol0 = # avol1 ∧ (∀ n. n < # avol0 → avol0[n] = avol1[n])

Rule argument

spec: array, inst: avolume name: Extension seq: ⊦ avol = avol0 ↔ # avol = # avol0 ∧ (∀ n. n < # avol → avol[n] = avol0[n]) subst: [avol0, avol] → [avol1, avol0] flags: <all paths>

Additional information

Used terms: avol1, avol0