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Proof step 3 from proof idcircle-concrete-write (previous step)

# avol = # avol0, n0 < # avol0, id○(avol, avol0[n, aleb], m) ⊦ avol[n0] = avol0[n0], m = n0, n0 = n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ id○(avol, avol0, n) ↔ # avol = # avol0 ∧ (∀ m. m < # avol ∧ m ≠ n → avol[m] = avol0[m])
Proof step 5:
# avol = # avol0[n, aleb], # avol = # avol0, n0 < # avol0, ∀ m0. m0 < # avol ∧ m0 ≠ m → avol[m0] = avol0[n, aleb][m0] ⊦ avol[n0] = avol0[n0], m = n0, n0 = n

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] → [m, avol0[n, aleb], avol] flags: <all paths>

Additional information

Used terms: m, avol0[n, aleb], avol