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Proof step 6 from proof id-circle-subarray-concrete-below (previous step)

# avol = # avol0, n1 < m0, n0 < n, id○(avol, avol0, n0), n + m + m0 ≤ # avol0 ⊦ avol[(n + m) + n1] = avol0[(n + m) + n1]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ id○(avol, avol0, n) ↔ # avol = # avol0 ∧ (∀ m. m < # avol ∧ m ≠ n → avol[m] = avol0[m])
Proof step 8:
# avol = # avol0, n0 < n, n1 < m0, n + m + m0 ≤ # avol0, ∀ m. m < # avol ∧ m ≠ n0 → avol[m] = avol0[m] ⊦ avol[(n + m) + n1] = avol0[(n + m) + n1]

Rule argument

spec: array-copy, inst: avolume name: Idexcept seq: ⊦ id○(avol, avol0, n) ↔ # avol = # avol0 ∧ (∀ m. m < # avol ∧ m ≠ n → avol[m] = avol0[m]) subst: [n, avol0, avol] → [n0, avol0, avol] flags: <all paths>

Additional information

Used terms: n0, avol0, avol