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Proof step 1 from proof valid-indices-append (conclusion)

⊦ valid-indices(ar, nx0 + nx1) ↔ valid-indices(ar, nx0) ∧ valid-indices(ar, nx1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ valid-indices(ar, nx) ↔ nx < # ar
Proof step 3:
⊦ nx0 + nx1 < # ar ↔ nx0 < # ar ∧ nx1 < # ar

Rule argument

Additional information

Used simplifier rules: valid-indices: ⊦ valid-indices(ar, nx) ↔ nx < # ar;