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Proof step 2 from proof id-idx-write (previous step)

# ar0 = # ar1 ⊦ (∀ n0. n0 < # ar1 → ar1[n0].elem = ar0[n, ar0[n].idx:= m][n0].elem) ↔ (∀ n. n < # ar1 → ar1[n].elem = ar0[n].elem)

User applied rule case distinction

And obtained the following new goals

Proof step 3:
# ar0 = # ar1, ∀ n0. n0 < # ar1 → ar1[n0].elem = ar0[n, ar0[n].idx:= m][n0].elem ⊦ ∀ n. n < # ar1 → ar1[n].elem = ar0[n].elem
Proof step 10:
# ar0 = # ar1, ∀ n. n < # ar1 → ar1[n].elem = ar0[n].elem ⊦ ∀ n0. n0 < # ar1 → ar1[n0].elem = ar0[n, ar0[n].idx:= m][n0].elem

Rule argument

pos: right 1

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