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Proof step 2 from proof keys-at (previous step)

n < # ax ⊦ keys(fs, ax)[n] = fs[ax[n]].key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n < # ax ⊦ keys(fs, ax)[n] = fs[ax[n]].key, ax = []

Rule argument

Additional information

Used simplifier rules: ⊦ # ax = 0 ↔ ax = []; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic