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Proof step 5 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 6:
# nσ ≠ ∞ ∧ ¬ nσ[n] < nσ[(# nσ).n - 1], min(nσ, nσ[n] + 1) = (# nσ).n, ⌜n⌝ < # nσ, mon<(nσ) ⊦ min(nσ, nσ[n] + 1) = n + 1, nσ = []
Proof step 13:
# nσ = ∞ ∨ nσ[n] < nσ[(# nσ).n - 1], ⌜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), ⌜n⌝ < # nσ, mon<(nσ) ⊦ min(nσ, nσ[n] + 1) = n + 1, nσ = []

Rule argument

pos: left 3

Proof step 5 from proof mininv-inverts-inner-succ (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information