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Proof step 16 from proof size-rmdup-del (previous step)

¬ a0 ∈ x0 -l a, # rmdup(x0) = m0 + 1, # rmdup(a0 ' + x0) = m + 1, a ∈ x0, ∀ a. a ∈ x0 → # rmdup(x0 -l a) = m0 ⊦ a = a0, # rmdup(a0 ' + (x0 -l a)) = m, x0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
# rmdup(x0) = m0 + 1, # rmdup(a0 ' + x0) = m + 1, a ∈ x0, ∀ a. a ∈ x0 → # rmdup(x0 -l a) = m0 ⊦ x0 = [], a = a0, 1 + # rmdup(x0 -l a) = m, a0 ∈ x0 -l a

Rule argument

Additional information

Used simplifier rules: len-02: ⊦ # a ' = 0 +1; from specification list%len: ⊦ #(x + y) = # x + # y; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list%rmdup-n: ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x); from specification list-dup