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Proof step 3 from proof subarray-avol-write (previous step)

# avol = main + m, n < m ⊦ subarray(avol[main + n, aleb], main, m) = subarray(avol, main, m)[n, aleb]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ avol = avol0 ↔ # avol = # avol0 ∧ (∀ n. n < # avol → avol[n] = avol0[n])
Proof step 5:
# avol = main + m, n < m ⊦ # subarray(avol[main + n, aleb], main, m) = # subarray(avol, main, m)[n, aleb] ∧ (∀ n0. n0 < # subarray(avol[main + n, aleb], main, m) → subarray(avol[main + n, aleb], main, m)[n0] = subarray(avol, main, m)[n, aleb][n0])

Rule argument

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

Additional information

Used terms: subarray(avol, main, m)[n, aleb], subarray(avol[main + n, aleb], main, m)