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Proof step 7 from proof map-if-at (previous step)

n < # ar ⊦ ar.mapIndices(ar.indicesWhere(φ), f)[n] = (φ(ar[n]) ⊃ f(ar[n]);ar[n]), valid-indices(ar, ar.indicesWhere(φ)) ∧ ¬ dups(ar.indicesWhere(φ)) ∧ n < # ar

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ valid-indices(ar, ar.indicesWhere(φ))
Proof step 9:
⊦ ¬ dups(ar.indicesWhere(φ))

Rule argument

spec: <toplevel> name: valid-indices-indiceswhere seq: ⊦ valid-indices(ar, ar.indicesWhere(φ)) subst: [φ, ar] → [φ, ar] flags: <all paths>

Additional information

Used simplifier rules: valid-indices-nodups: ⊦ ¬ dups(ar.indicesWhere(φ)); Used terms: φ, ar