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Proof step 13 from proof stutf-alltaken (previous step)

nσ[0] = 0, nσ[m0] < nσ[m0 + 1], nσ[m0] < n, ⌜m0⌝ < # nσ, ⌜m0⌝ + ⌜1⌝ < # nσ, n ≤ nσ[m0 + 1], ∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n + 1] = nσ[n] ∨ nσ[n + 1] = nσ[n] + 1, m0 ≤ nσ[m0] → m ≤ nσ[m] ∧ nσ[m] = m0 ⊦ n = 0, nσ[m0 + 1] = 0, nσ = [], ∃ m. m ≤ m0 + 1 ∧ nσ[m] = n

User applied rule all left

And obtained the following new goals

Proof step 14:
nσ[0] = 0, nσ[m0] < nσ[m0 + 1], nσ[m0] < n, ⌜m0⌝ < # nσ, ⌜m0⌝ + ⌜1⌝ < # nσ, n ≤ nσ[m0 + 1], ⌜m0⌝ + ⌜1⌝ < # nσ → nσ[m0 + 1] = nσ[m0] ∨ nσ[m0 + 1] = nσ[m0] + 1, m0 ≤ nσ[m0] → m ≤ nσ[m] ∧ nσ[m] = m0 ⊦ n = 0, nσ[m0 + 1] = 0, nσ = [], ∃ m. m ≤ m0 + 1 ∧ nσ[m] = n

Rule argument

pos: left 7 terms: m0 abort: F discard: T computed: T

Additional information

Used terms: m0