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Proof step 17 from proof mininv-stays-if-not-taken (previous step)

⌜min(nσ, n)⌝ < # nσ, ⌜min(nσ, n + 1)⌝ < # nσ, n < nσ[min(nσ, n + 1)], mon<(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 = ∞ ∨ ¬ nσ[(# nσ).n - 1] < n, # nσ = ∞ ∨ n < nσ[(# nσ).n - 1] ⊦ min(nσ, n + 1) = min(nσ, n), nσ = []

User applied rule all left

And obtained the following new goals

Proof step 18:
n < nσ[min(nσ, n + 1)], ⌜min(nσ, n + 1)⌝ < # nσ, ⌜min(nσ, n)⌝ < # nσ, mon<(nσ), n ≤ nσ[min(nσ, n)], ⌜min(nσ, n + 1)⌝ < # nσ ∧ n ≤ nσ[min(nσ, n + 1)] → min(nσ, n) ≤ min(nσ, n + 1), ∀ m. ⌜m⌝ < # nσ ∧ n < nσ[m] → min(nσ, n + 1) ≤ m, ∀ m. ⌜m⌝ < # nσ → nσ[m] ≠ n, ∀ m. ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → min(nσ, n) ≤ m, # nσ = ∞ ∨ n < nσ[(# nσ).n - 1], # nσ = ∞ ∨ ¬ nσ[(# nσ).n - 1] < n ⊦ min(nσ, n + 1) = min(nσ, n), nσ = []

Rule argument

pos: left 6 terms: min(nσ, n + 1) abort: F discard: F computed: T

Additional information

Used terms: min(nσ, n + 1)