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Proof step 6 from proof diff-twice-union (previous step)

a ∈ y, ∀ y, z. (x0 \ y) \ z = x0 \ rmdup(y + z) ⊦ (x0 \ y) \ z = (a ' + x0) \ rmdup(y + z)

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 7:
a ∈ rmdup(y + z), a ∈ y, ∀ y, z. (x0 \ y) \ z = x0 \ rmdup(y + z) ⊦ (x0 \ y) \ z = (a ' + x0) \ rmdup(y + z)

Rule argument

fma: a ∈ rmdup(y + z)

Additional information

Used simplifier rules: diff-n: ⊦ ¬ a ∈ y → (a ' + x) \ y = a + (x \ y);%c: ⊦ a + x = a ' + x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%rm-in: ⊦ a ∈ rmdup(x + y) ↔ a ∈ x ∨ a ∈ y; from specification list-dup Used formulas: a ∈ rmdup(y + z)