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Proof step 20 from proof rm-size-01 (previous step)

a ∈ x0, ∀ a, y. a ∈ x0 → # rmdup(x0 + a ' + y) = # rmdup(x0 + y) ⊦ 1 + # rmdup(x0 + a ' + y) = # (a0 ∈ x0 + y ⊃ rmdup(x0 + y);a0 ' + rmdup(x0 + y)), a0 ∈ y, a0 ∈ x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
a ∈ x0, ∀ a, y. a ∈ x0 → # 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-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ # a ' = 0 +1; (s)% ⊦ #(x + y) = # x + # y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)