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Proof step 12 from proof prepost-fix-ecs (previous step)

n0 < # wlar1, n0 < # wlar1.mapIndices(nx4, λ wle. wle.ec:= n), valid-indices(wlar1, nx0), valid-indices(wlar1.mapIndices(nx4, λ wle. wle.ec:= n), nx4), valid-indices(wlar1, nx4) ⊦ wlar1.mapIndices(nx4, λ wle. wle.ec:= n)[n0, wlar1.mapIndices(nx4, λ wle. wle.ec:= n)[n0].ec:= n] = wlar1.mapIndices(nx4 + n0 ', λ wle. wle.ec:= n), dups(nx0), dups(nx4), dups(nx4 + nx0), n0 ∈ nx4, n0 ∈ nx0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ ¬ n ∈ nx ∧ valid-indices(wlar, nx) ∧ n < # wlar → wlar.mapIndices(nx + n ', f0) = wlar.mapIndices(nx, f0)[n, f0(wlar[n])]
Proof step 14:
n0 < # wlar1.mapIndices(nx4, λ wle. wle.ec:= n), n0 < # wlar1, valid-indices(wlar1.mapIndices(nx4, λ wle. wle.ec:= n), nx4), valid-indices(wlar1, nx0), valid-indices(wlar1, nx4) ⊦ wlar1.mapIndices(nx4, λ wle. wle.ec:= n)[n0, wlar1.mapIndices(nx4, λ wle. wle.ec:= n)[n0].ec:= n] = wlar1.mapIndices(nx4, λ wle. wle.ec:= n)[n0, wlar1[n0].ec:= n], dups(nx4 + nx0), dups(nx4), dups(nx0), n0 ∈ nx0, n0 ∈ nx4

Rule argument

spec: array-indices, inst: wlarray-base name: map-indices-append seq: ⊦ ¬ n ∈ nx ∧ valid-indices(wlar, nx) ∧ n < # wlar → wlar.mapIndices(nx + n ', f0) = wlar.mapIndices(nx, f0)[n, f0(wlar[n])] subst: [f0, n, nx, wlar] → [λ wle. wle.ec:= n, n0, nx4, wlar1] flags: <all paths>

Additional information

Used terms: λ wle. wle.ec:= n, n0, nx4, wlar1