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Proof step 8 from proof valid-indices-append (previous step)

⊦ (∀ n. n ∈ nx0 ∨ n ∈ nx1 → n < # ar) ↔ (∀ n. n ∈ nx0 → n < # ar) ∧ nx1 < # ar

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ nx < m ↔ (∀ n. n ∈ nx → n < m)
Proof step 10:
⊦ (∀ n. n ∈ nx0 ∨ n ∈ nx1 → n < # ar) ↔ (∀ n. n ∈ nx0 → n < # ar) ∧ (∀ n. n ∈ nx1 → n < # ar)

Rule argument

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

Additional information

Used terms: # ar, nx1