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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
1 + # x0 < # rmdup(a ' + x0), # rmdup(x0) ≤ # x0 ⊦ x0 = []

Rule argument

Additional information

Used simplifier rules: rm-empty: ⊦ rmdup(x) = [] ↔ x = [];%rm-one: ⊦ rmdup(a ') = a ';% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ x + [] = x; (s)% ⊦ # [] = 0; (s)% ⊦ # x = 0 ↔ x = []; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ # a ' = 0 +1; (s)% ⊦ #(x + y) = # x + # y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ' + x ≠ []; (s)% ⊦ a + x = a ' + x; (s)