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Proof step 20 from proof size-rmdup-del (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# rmdup(x0) = m0 + 1, a ∈ x0, ∀ a. a ∈ x0 → # rmdup(x0 -l a) = m0 ⊦ # rmdup(x0 -l a) = m0, x0 = [], a0 ∈ x0 -l a, a0 ∈ x0

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 = a ' + x; (s)% ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x); (s)