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Proof step 6 from proof subset-insert-01 (previous step)

c ∈ s ⊦ a0 = a, c = b, a ∈ s, a0 ∈ s, s ⊆ s ++ a ++ a0 ++ b ++ c

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 7:
c ∈ s, b ∈ s ++ a ++ a0 ⊦ a0 = a, c = b, a0 ∈ s, a ∈ s, s ⊆ s ++ a ++ a0 ++ b ++ c
Proof step 10:
c ∈ s ⊦ a0 = a, c = b, a0 ∈ s, a ∈ s, b ∈ s ++ a ++ a0, s ⊆ s ++ a ++ a0 ++ b ++ c

Rule argument

fma: b ∈ s ++ a ++ a0

Additional information

Used formulas: b ∈ s ++ a ++ a0