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Proof step 2 from proof union-write (previous step)

n < m, disj(asar, 0, m), m ≤ # asar ⊦ union(asar[n, as], 0, m) = (union(asar, 0, m) \ asar[n]) ∪ as

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n < m, n < # asar, disj(asar, 0, m), m ≤ # asar ⊦ union(asar[n, as], 0, m) = (union(asar, 0, m) \ asar[n]) ∪ as

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic