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Proof step 3 from proof map-ifn-0 (previous step)

⊦ # ar.mapIf(φ, f, 0) = # ar ∧ (∀ n. n < # ar.mapIf(φ, f, 0) → ar.mapIf(φ, f, 0)[n] = ar[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
n ≤ # ar ⊦ # ar.mapIf(φ, f, n) = # ar
Proof step 5:
n < # ar ⊦ ar.mapIf(φ, f, 0)[n] = ar[n]

Rule argument

Additional information

Used simplifier rules: map-ifn-size: n ≤ # ar ⊦ # ar.mapIf(φ, f, n) = # ar;% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ 0 ≤ m; (s)