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Proof step 1 from proof id-idx-write (conclusion)

⊦ id-idx(ar1, ar0[n, ar0[n].idx:= m]) ↔ id-idx(ar1, ar0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
# 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)

Rule argument

Additional information

Used simplifier rules: id-idx: ⊦ id-idx(ar1, ar0) ↔ # ar0 = # ar1 ∧ (∀ n. n < # ar0 → ar1[n].elem = ar0[n].elem);% ⊦ # ar[n, ei] = # ar; (s)