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

n ≤ # ar ⊦ # ar.mapIndices(ar.indicesWhere(φ, n), f) = # ar

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ valid-indices(ar, nx) → # ar.mapIndices(nx, f) = # ar
Proof step 5:
n ≤ # ar ⊦ # ar.mapIndices(ar.indicesWhere(φ, n), f) = # ar, valid-indices(ar, ar.indicesWhere(φ, n))

Rule argument

spec: <toplevel> name: map-indices-size seq: ⊦ valid-indices(ar, nx) → # ar.mapIndices(nx, f) = # ar subst: [f, nx, ar] → [f, ar.indicesWhere(φ, n), ar] flags: <all paths>

Additional information

Used terms: f, ar.indicesWhere(φ, n), ar