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Proof step 16 from proof prefixn-prefixn (previous step)

(m ≤ # x ⊃ firstn(m, x);x) = y + z, # x < (# y < m ⊃ # y;m) ⊦ y = x

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: m ≤ # x

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ x = x + y ↔ y = []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ #(x + y) = # x + # y; (s)% ⊦ ¬ m < n → ¬ m + m0 < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ m + n < m; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ # x = 0 ↔ x = []; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ ¬ n < n; (s) Used formulas: m ≤ # x