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Proof step 11 from proof valid-indices-nonrec (previous step)

∀ ar. nx0 < # ar ↔ (∀ n. n ∈ nx0 → n < # ar), ∀ n. n = m ∨ n ∈ nx0 → n < # ar ⊦ m ' + nx0 < # ar

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ m ' + nx < n ↔ m < n ∧ nx < n
Proof step 13:
∀ n. n = m ∨ n ∈ nx0 → n < # ar, ∀ ar. nx0 < # ar ↔ (∀ n. n ∈ nx0 → n < # ar) ⊦ m < # ar ∧ nx0 < # ar

Rule argument

spec: nat-list-less name: ls-rec seq: ⊦ m ' + nx < n ↔ m < n ∧ nx < n subst: [n, nx, m] → [# ar, nx0, m] flags: <all paths>

Additional information

Used terms: # ar, nx0, m