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Proof step 10 from proof del1-01 (previous step)

∀ y, a. filter(rmdup(x0), y -1l a) = filter(rmdup(x0), y) ∨ a ∈ x0 ⊦ a = a0, filter(a0 ' + rmdup(x0), y -1l a) = filter(a0 ' + rmdup(x0), y), a0 ∈ x0, a ∈ x0

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 11:
a0 ∈ y -1l a, ∀ y, a. filter(rmdup(x0), y -1l a) = filter(rmdup(x0), y) ∨ a ∈ x0 ⊦ a = a0, filter(a0 ' + rmdup(x0), y -1l a) = filter(a0 ' + rmdup(x0), y), a0 ∈ x0, a ∈ x0
Proof step 13:
∀ y, a. filter(rmdup(x0), y -1l a) = filter(rmdup(x0), y) ∨ a ∈ x0 ⊦ a0 ∈ y -1l a, a = a0, filter(a0 ' + rmdup(x0), y -1l a) = filter(a0 ' + rmdup(x0), y), a0 ∈ x0, a ∈ x0

Rule argument

fma: a0 ∈ y -1l a

Additional information

Used formulas: a0 ∈ y -1l a