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Proof step 17 from proof lsleninv-1 (previous step)

m1 < nσ[m], ⌜m⌝ < # nσ, stutf(nσ), m1 + 1 < nσ[m], m0 ≤ m, m1 < nσ[m0], nσ[m0] < nσ[m], (# nσ = ∞ ⊃ nσ[m2] = m1 ∧ (∀ m0. m2 < m0 → nσ[m0] = nσ[m2] + 1);nσ[(# nσ).n - 1] = m1) ⊦

User applied rule case distinction

And obtained the following new goals

Proof step 18:
# nσ = ∞, nσ[m2] = m1 ∧ (∀ m0. m2 < m0 → nσ[m0] = nσ[m2] + 1), m1 < nσ[m], ⌜m⌝ < # nσ, stutf(nσ), m1 + 1 < nσ[m], m0 ≤ m, m1 < nσ[m0], nσ[m0] < nσ[m] ⊦
Proof step 23:
# nσ ≠ ∞, nσ[(# nσ).n - 1] = m1, m1 < nσ[m], ⌜m⌝ < # nσ, stutf(nσ), m1 + 1 < nσ[m], m0 ≤ m, m1 < nσ[m0], nσ[m0] < nσ[m] ⊦

Rule argument

pos: left 8

Proof step 17 from proof lsleninv-1 (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information