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

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

User applied rule case distinction

And obtained the following new goals

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

Rule argument

pos: left 3

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

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information