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Proof step 64 from proof leninv-succ (previous step)

nσ[(m1 + 1) + m] = nσ[m] + 1, # nσ = ∞, stutf(nσ), nσ[m1 + m] = nσ[m] + 1 ∧ m1 ≠ 0 → m ≤ m0 ∧ m0 < m1 + m ∧ nσ[m] = nσ[m0] ∧ nσ[m0 + 1] = nσ[m0] + 1 ⊦ nσ[m] = nσ[m + 1], ∃ m0. m ≤ m0 ∧ ¬ m1 + m < m0 ∧ nσ[m] = nσ[m0] ∧ nσ[m0 + 1] = nσ[m0] + 1

User applied rule case distinction

And obtained the following new goals

Proof step 65:
nσ[(m1 + 1) + m] = nσ[m] + 1, # nσ = ∞, stutf(nσ) ⊦ nσ[m1 + m] = nσ[m] + 1 ∧ m1 ≠ 0, nσ[m] = nσ[m + 1], ∃ m0. m ≤ m0 ∧ ¬ m1 + m < m0 ∧ nσ[m] = nσ[m0] ∧ nσ[m0 + 1] = nσ[m0] + 1
Proof step 71:
m ≤ m0 ∧ m0 < m1 + m ∧ nσ[m] = nσ[m0] ∧ nσ[m0 + 1] = nσ[m0] + 1, nσ[(m1 + 1) + m] = nσ[m] + 1, # nσ = ∞, stutf(nσ) ⊦ nσ[m] = nσ[m + 1], ∃ m0. m ≤ m0 ∧ ¬ m1 + m < m0 ∧ nσ[m] = nσ[m0] ∧ nσ[m0 + 1] = nσ[m0] + 1

Rule argument

pos: left 4

Proof step 64 from proof leninv-succ (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information