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Proof step 9 from proof stutf-notbig (previous step)

nσ[0] = 0, n0 + 1 < nσ[n0 + 1], ⌜n0⌝ + ⌜1⌝ < # nσ, ⌜n0⌝ < # nσ, nσ[n0] ≤ n0, ∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n + 1] = nσ[n] ∨ nσ[n + 1] = nσ[n] + 1 ⊦ nσ = []

User applied rule all left

And closed the goal!

Rule argument

pos: left 6 terms: n0 abort: F discard: F computed: T

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ m = m + n ↔ n = 0; (s)% ⊦ ¬ m + n < m; (s) Used terms: n0