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Proof step 6 from proof diffone-nodupssize (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 7:
a ∈ x0, ∀ m0, a1. # x0 = m0 + 1 ∧ a1 ∈ x0 → #(x0 \ a1 ') = m0 ∨ x0 = [] ⊦ a0 ∈ a ', #((a0 ' + x0) \ a ') = # x0, dups(x0), a0 ∈ x0

Rule argument

fma: a0 ∈ a '

Additional information

Used simplifier rules: diff-y: ⊦ a ∈ y → (a ' + x) \ y = x \ y;%a: ⊦ (x + y) + z = x + y + z; from specification list%in-17: ⊦ a ∈ b ' ↔ a = b; from specification list Used formulas: a0 ∈ a '