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Proof step 8 from proof diffone-nodupssize (previous step)

a ∈ x0, ∀ m0, a1. # x0 = m0 + 1 ∧ a1 ∈ x0 → #(x0 \ a1 ') = m0 ∨ x0 = [] ⊦ #(x0 \ a ') + 1 = # x0, dups(x0), a0 ∈ x0

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 9:
a ∈ x0, ∀ m0, a1. # x0 = m0 + 1 ∧ a1 ∈ x0 → #(x0 \ a1 ') = m0 ∨ x0 = [] ⊦ x0 = [], #(x0 \ a ') + 1 = # x0, dups(x0), a0 ∈ x0

Rule argument

fma: x0 = []

Additional information

Used simplifier rules: diff-e: ⊦ [] \ y = [];%size-01: ⊦ # [] = 0; from specification list-data%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%in-empty: ⊦ ¬ a ∈ []; from specification list Used formulas: x0 = []