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Proof step 7 from proof mininv-stays-if-not-taken (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 8:
min(nσ, n + 1) = (# nσ).n, mon<(nσ), (# nσ ≠ ∞ ∧ nσ[(# nσ).n - 1] < n ⊃ min(nσ, n) = (# nσ).n ;⌜min(nσ, n)⌝ < # nσ ∧ n ≤ nσ[min(nσ, n)] ∧ (∀ m. ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → min(nσ, n) ≤ m) ), ∀ m. ⌜m⌝ < # nσ → nσ[m] ≠ n ⊦ # nσ = ∞, min(nσ, n + 1) = min(nσ, n), nσ = [], n < nσ[(# nσ).n - 1]
Proof step 14:
⌜min(nσ, n + 1)⌝ < # nσ, n < nσ[min(nσ, n + 1)], mon<(nσ), (# nσ ≠ ∞ ∧ nσ[(# nσ).n - 1] < n ⊃ min(nσ, n) = (# nσ).n ;⌜min(nσ, n)⌝ < # nσ ∧ n ≤ nσ[min(nσ, n)] ∧ (∀ m. ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → min(nσ, n) ≤ m) ), ∀ m. ⌜m⌝ < # nσ → nσ[m] ≠ n, ∀ m. ⌜m⌝ < # nσ ∧ n < nσ[m] → min(nσ, n + 1) ≤ m, # nσ = ∞ ∨ n < nσ[(# nσ).n - 1] ⊦ min(nσ, n + 1) = min(nσ, n), nσ = []

Rule argument

pos: left 3

Proof step 7 from proof mininv-stays-if-not-taken (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information