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Proof step 5 from proof idexcept-extract-left (previous step)

# ar0 = # ar1 ⊦ (∀ m. m < # ar1 ∧ m ≠ n → ar0[m] = ar1[m]) ↔ (∀ n0. n0 < # ar1 → ar0[n0] = ar1[n, ar0[n]][n0])

User applied rule case distinction

And obtained the following new goals

Proof step 6:
∀ m. m < # ar1 ∧ m ≠ n → ar0[m] = ar1[m], # ar0 = # ar1 ⊦ ∀ n0. n0 < # ar1 → ar0[n0] = ar1[n, ar0[n]][n0]
Proof step 10:
∀ n0. n0 < # ar1 → ar0[n0] = ar1[n, ar0[n]][n0], # ar0 = # ar1 ⊦ ∀ m. m < # ar1 ∧ m ≠ n → ar0[m] = ar1[m]

Rule argument

pos: right 1

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