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Proof step 3 from proof rm-size-05 (previous step)

# x0 < # rmdup(x0) → x0 = [], #(a + x0) < # rmdup(a + x0) ⊦ a + x0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: rm-empty: ⊦ rmdup(x) = [] ↔ x = [];%rm-one: ⊦ rmdup(a ') = a ';%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%len-02: ⊦ # a ' = 0 +1; from specification list%app: ⊦ x + [] = x; from specification list%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%size-01: ⊦ # [] = 0; from specification list-data%l: ⊦ # x = 0 ↔ x = []; from specification list-data%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%succ: ⊦ m +1 = m + 1; from specification nat-basic2%len-05: ⊦ #(a ' + x) = (# x)+1; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%e-01: ⊦ a ' + x ≠ []; from specification list%c: ⊦ a + x = a ' + x; from specification list