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Proof step 11 from proof monls-ls (previous step)

⌜m1⌝ + ⌜m⌝ < # nσ, ⌜m1⌝ + ⌜1⌝ + ⌜m⌝ < # nσ, nσ[(m1 + 1) + m] ≤ nσ[m], ∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1], ¬ nσ[m1 + m] ≤ nσ[m] ∨ m1 = 0 ⊦

User applied rule case distinction

And obtained the following new goals

Proof step 12:
⌜m1⌝ + ⌜1⌝ + ⌜m⌝ < # nσ, ⌜m1⌝ + ⌜m⌝ < # nσ, nσ[(m1 + 1) + m] ≤ nσ[m], ∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1] ⊦ nσ[m1 + m] ≤ nσ[m]
Proof step 14:
m1 = 0, ⌜m1⌝ + ⌜1⌝ + ⌜m⌝ < # nσ, ⌜m1⌝ + ⌜m⌝ < # nσ, nσ[(m1 + 1) + m] ≤ nσ[m], ∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1] ⊦

Rule argument

pos: left 5

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