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Proof step 6 from proof mininv-inverts-inner-succ (previous step)

⌜n⌝ < # nσ, mon<(nσ), (# nσ ≠ ∞ ∧ ¬ nσ[n] < nσ[(# nσ).n - 1] ⊃ min(nσ, nσ[n] + 1) = (# nσ).n ;⌜min(nσ, nσ[n] + 1)⌝ < # nσ ∧ nσ[n] < nσ[min(nσ, nσ[n] + 1)] ∧ (∀ m. ⌜m⌝ < # nσ ∧ nσ[n] < nσ[m] → min(nσ, nσ[n] + 1) ≤ m) ) ⊦ min(nσ, nσ[n] + 1) = n + 1, nσ = []

User applied rule case distinction

And obtained the following new goals

Proof step 7:
min(nσ, nσ[n] + 1) = (# nσ).n, ⌜n⌝ < # nσ, mon<(nσ) ⊦ # nσ = ∞, min(nσ, nσ[n] + 1) = n + 1, nσ = [], nσ[n] < nσ[(# nσ).n - 1]
Proof step 14:
⌜n⌝ < # nσ, ⌜min(nσ, nσ[n] + 1)⌝ < # nσ, nσ[n] < nσ[min(nσ, nσ[n] + 1)], mon<(nσ), ∀ m. ⌜m⌝ < # nσ ∧ nσ[n] < nσ[m] → min(nσ, nσ[n] + 1) ≤ m, # nσ = ∞ ∨ nσ[n] < nσ[(# nσ).n - 1] ⊦ min(nσ, nσ[n] + 1) = n + 1, nσ = []

Rule argument

pos: left 3

Proof step 6 from proof mininv-inverts-inner-succ (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information