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Proof step 5 from proof rm-size-05 (previous step)

1 + # x0 < # rmdup(a ' + x0), # rmdup(x0) ≤ # x0 ⊦ x0 = []

Heuristic cut applied rule cut formula

And closed the goal!

Rule argument

fma: a ∈ x0

Additional information

Used simplifier rules: rmdup-y: ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x);%rm-empty: ⊦ rmdup(x) = [] ↔ x = [];%rmdup-n: ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x);% ⊦ a + x = a ' + x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ #(x + y) = # x + # y; (s)% ⊦ # a ' = 0 +1; (s)% ⊦ 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% ⊦ # x = 0 ↔ x = []; (s)% ⊦ ¬ m + n < m; (s) Used formulas: a ∈ x0