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Proof step 4 from proof restn-nonempty (previous step)

restn(n, a ' + a0 ' + x0) = [], n ≤ # x0, (∃ n, a. restn(n, a ' + x0) = [] ∧ n < # x0) → x0 = [] ⊦

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 5:
restn(n, a ' + a0 ' + x0) = [], n ≤ # x0, (∃ n, a. restn(n, a ' + x0) = [] ∧ n < # x0) → x0 = [] ⊦ x0 = []

Rule argument

fma: x0 = []

Additional information

Used simplifier rules: restN-zero: ⊦ restn(0, x) = x;%app: ⊦ x + [] = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%size-01: ⊦ # [] = 0; from specification list-data%lez-01: ⊦ m ≤ 0 ↔ m = 0; from specification nat%zero-01: ⊦ ¬ m < 0; from specification nat-basic1%app-02-ant: ⊦ ¬ x + y ≠ [] ↔ x = [] ∧ y = []; from specification list%e: ⊦ a ' ≠ []; from specification list Used formulas: x0 = []