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Proof step 7 from proof keys-at (previous step)

n ≤ # ax0, ∀ n, fs. n < # ax0 → keys(fs, ax0)[n] = fs[ax0[n]].key ∨ ax0 = [] ⊦ keys(fs, ax0)[n - # fs[adr].key '] = fs[(adr ' + ax0)[n]].key, n < # fs[adr].key '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
n ≤ # ax0, ∀ n, fs. n < # ax0 → keys(fs, ax0)[n] = fs[ax0[n]].key ∨ ax0 = [] ⊦ keys(fs, ax0)[n - 1] = fs[(adr ' + ax0)[n]].key, n = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m < 1 ↔ m = 0; (s)% ⊦ # key ' = 0 +1; (s)