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Proof step 28 from proof rm-size-01 (previous step)

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

Heuristic cut applied rule cut formula

And closed the goal!

Rule argument

fma: a0 ∈ y

Additional information

Used simplifier rules: rm-size-02: ⊦ a ∈ y → # rmdup(x + a ' + y) = # rmdup(x + y);%rm-size: ⊦ ¬ a ∈ x ∧ ¬ a ∈ y → # rmdup(x + a ' + y) = # rmdup(x + y) + 1;%a: ⊦ (x + y) + z = x + y + z; from specification list%len-05: ⊦ #(a ' + x) = (# x)+1; from specification list%succ: ⊦ m +1 = m + 1; from specification nat-basic2%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used formulas: a0 ∈ y