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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H0: SNoCutP x0 x1.
Assume H1: SNoCutP x2 x3.
Assume H2: ∀ x4 . x4 ∈ x0 ⟶ SNoLt x4 (SNoCut x2 x3).
Assume H3: ∀ x4 . x4 ∈ x1 ⟶ SNoLt (SNoCut x2 x3) x4.
Assume H4: ∀ x4 . x4 ∈ x2 ⟶ SNoLt x4 (SNoCut x0 x1).
Assume H5: ∀ x4 . x4 ∈ x3 ⟶ SNoLt (SNoCut x0 x1) x4.
Claim L6: SNo (SNoCut x0 x1)
Apply SNoCutP_SNo_SNoCut with x0, x1.
The subproof is completed by applying H0.
Claim L7: SNo (SNoCut x2 x3)
Apply SNoCutP_SNo_SNoCut with x2, x3.
The subproof is completed by applying H1.
Apply SNoLe_antisym with SNoCut x0 x1, SNoCut x2 x3 leaving 4 subgoals.
The subproof is completed by applying L6.
The subproof is completed by applying L7.
Apply SNoCut_Le with x0, x1, x2, x3 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H5.
Apply SNoCut_Le with x2, x3, x0, x1 leaving 4 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
The subproof is completed by applying H4.
The subproof is completed by applying H3.
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