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Proof step 21 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(x0 -l a) = m, x0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
# rmdup(x0) = m0 + 1, a0 ∈ x0, a ∈ x0, ∀ a. a ∈ x0 → # rmdup(x0 -l a) = m0 ⊦ x0 = [], # rmdup(x0 -l a) = m0, a = a0

Rule argument

Additional information

Used simplifier rules: in-01: ⊦ a ∈ x -l b → a ∈ x ∧ a ≠ b;%in: ⊦ a ∈ x ∧ a ≠ b → a ∈ x -l b;%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%rmdup-y: ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x); from specification list-dup