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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
∀ a, y. # rmdup(x0 + a ' + y) = # rmdup(x0 + y) + 1 ∨ a ∈ y ∨ a ∈ x0 ⊦ a = a0, # rmdup(x0 + a ' + y) = # rmdup(x0 + y) + 1, a ∈ y, a ∈ x0, a0 ∈ x0, a0 ∈ y

Rule argument

Additional information

Used simplifier rules: add-num-01: n < n0 ⊦ m + (* n) = m0 + (* n0) ↔ m = m0 + (n0 - n); from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; 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