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Proof step 4 from proof rm-size-05 (previous step)

# x0 + 1 < # 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);%c: ⊦ a + x = a ' + x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%len-05: ⊦ #(a ' + x) = (# x)+1; from specification list%succ: ⊦ m +1 = m + 1; from specification nat-basic2%ls-add-not-01: ⊦ m ≤ m0 ∧ n ≤ n0 → ¬ m0 + n0 < m + n; from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%l: ⊦ # x = 0 ↔ x = []; from specification list-data%l-02: ⊦ ¬ m + n < m; from specification nat-basic2 Used formulas: a ∈ x0