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Proof step 3 from proof valid-indices-append (previous step)

⊦ nx0 + nx1 < # ar ↔ nx0 < # ar ∧ nx1 < # ar

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ nx < m ↔ (∀ n. n ∈ nx → n < m)
Proof step 5:
⊦ (∀ n. n ∈ nx0 + nx1 → n < # ar) ↔ nx0 < # ar ∧ nx1 < # ar

Rule argument

spec: nat-list-less name: ls-ext seq: ⊦ nx < m ↔ (∀ n. n ∈ nx → n < m) subst: [m, nx] → [# ar, nx0 + nx1] flags: <all paths>

Additional information

Used terms: # ar, nx0 + nx1