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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: valid-indices-nodups-h: ⊦ n ≤ # ar → ¬ dups(ar.indicesWhere(φ, n)); Used terms: m, φ, ar