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Proof step 1 from proof monls-notsmall (conclusion)

⊦ mon<(nσ) ∧ nσ[0] = 0 ∧ ⌜n + 1⌝ < # nσ → (¬ n < nσ[n + 1] ↔ false)

User applied rule structural induction

And obtained the following new goals

Proof step 2:
⊦ mon<(nσ) ∧ nσ[0] = 0 ∧ ⌜0 + 1⌝ < # nσ → (¬ 0 < nσ[0 + 1] ↔ false)
Proof step 6:
∀ nσ. mon<(nσ) ∧ nσ[0] = 0 ∧ ⌜n0 + 1⌝ < # nσ → (¬ n0 < nσ[n0 + 1] ↔ false) ⊦ mon<(nσ) ∧ nσ[0] = 0 ∧ ⌜n0 +1 + 1⌝ < # nσ → (¬ n0 +1 < nσ[n0 +1 + 1] ↔ false)

Rule argument

indvar: n

Additional information

Used simplifier rules: nat freely generated by 0, +1;;