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Proof step 68 from proof leninv-succ (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 69:
nσ[0] = 0, # nσ = ∞, nσ[(m1 + 1) + m] = nσ[m] + 1, nσ[m + 1] = nσ[m] ∨ nσ[m + 1] = nσ[m] + 1 ⊦ nσ = [], nσ[m] = nσ[m + 1], ∃ m0. m ≤ m0 ∧ ¬ m1 + m < m0 ∧ nσ[m] = nσ[m0] ∧ nσ[m0 + 1] = nσ[m0] + 1, nσ[m1 + m] = nσ[m] + 1 ∧ m1 ≠ 0

Rule argument

pos: left 4 terms: m abort: F discard: T computed: T

Additional information

Used terms: m