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

⊦ id-idx(ar1[m, ar1[m].idx:= m0], ar0) ↔ id-idx(ar1, ar0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
# ar0 = # ar1 ⊦ (∀ n. n < # ar1 → ar1[m, ar1[m].idx:= m0][n].elem = ar0[n].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)