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Proof step 2 from proof monls-notsmall (previous step)

nσ[0] = 0, ⌜n + 1⌝ < # nσ, mon<(nσ) ⊦ n < nσ[n + 1] ↔ true

User applied rule structural induction

And obtained the following new goals

Proof step 3:
nσ[0] = 0, ⌜0 + 1⌝ < # nσ, mon<(nσ) ⊦ 0 < nσ[0 + 1] ↔ true
Proof step 7:
nσ[0] = 0, ⌜n0 +1 + 1⌝ < # nσ, mon<(nσ), ∀ nσ. nσ[0] = 0 ∧ ⌜n0 + 1⌝ < # nσ ∧ mon<(nσ) → (n0 < nσ[n0 + 1] ↔ true) ⊦ n0 +1 < nσ[n0 +1 + 1] ↔ true

Rule argument

indvar: n

Additional information

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