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Proof step 18 from proof lsleninv-1 (previous step)

m1 + 1 < nσ[m], ⌜m⌝ < # nσ, m1 < nσ[m], m1 < nσ[m0], nσ[m0] < nσ[m], stutf(nσ), m0 ≤ 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 19:
# nσ = ∞, nσ[m2] = m1, nσ[m0] < nσ[m], m1 < nσ[m0], m1 < nσ[m], ⌜m⌝ < # nσ, m1 + 1 < nσ[m], stutf(nσ), m0 ≤ m, ∀ m0. m2 < m0 → nσ[m0] = nσ[m2] + 1 ⊦
Proof step 24:
nσ[(# nσ).n - 1] = m1, nσ[m0] < nσ[m], m1 < nσ[m0], m1 < nσ[m], ⌜m⌝ < # nσ, m1 + 1 < nσ[m], stutf(nσ), m0 ≤ m ⊦ # nσ = ∞

Rule argument

pos: left 8

Proof step 18 from proof lsleninv-1 (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information