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

n < # ar, m ≤ # ar ⊦ ar.mapIf(φ, f, m)[n] = (n < m ∧ φ(ar[n]) ⊃ f(ar[n]);ar[n])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ar.mapIf(φ, f, n) = ar.mapIndices(ar.indicesWhere(φ, n), f)
Proof step 5:
n < # ar, m ≤ # ar ⊦ ar.mapIndices(ar.indicesWhere(φ, m), f)[n] = (n < m ∧ φ(ar[n]) ⊃ f(ar[n]);ar[n])

Rule argument

spec: <toplevel> name: mapifn-def seq: ⊦ ar.mapIf(φ, f, n) = ar.mapIndices(ar.indicesWhere(φ, n), f) subst: [n, f, φ, ar] → [m, f, φ, ar] flags: <all paths>

Additional information

Used terms: m, f, φ, ar