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Proof step 13 from proof rm-size-02 (previous step)

¬(a0 ∈ x0 ∨ a0 ∈ y), a ∈ y, ∀ a, y. a ∈ y → # rmdup(x0 + a ' + y) = # rmdup(x0 + y) ⊦ #(a0 ' + rmdup(x0 + a ' + y)) = # (a0 ∈ x0 ∨ a0 ∈ y ⊃ rmdup(x0 + y);a0 ' + rmdup(x0 + y))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
a ∈ y, ∀ a, y. a ∈ y → # rmdup(x0 + a ' + y) = # rmdup(x0 + y) ⊦ # rmdup(x0 + a ' + y) = # rmdup(x0 + y), a0 ∈ x0, a0 ∈ y

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2%a: ⊦ (x + y) + z = x + y + z; from specification list%succ: ⊦ m +1 = m + 1; from specification nat-basic2%len-05: ⊦ #(a ' + x) = (# x)+1; from specification list