Let x0 of type ι be given.
Let x1 of type ι be given.
Apply ordinal_In_Or_Subq with
x1,
x0,
x0 ⊆ x1 leaving 4 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Assume H3: x1 ∈ x0.
Apply FalseE with
x0 ⊆ x1.
Apply SNoLt_irref with
x0.
Apply SNoLeLt_tra with
x0,
x1,
x0 leaving 5 subgoals.
Apply ordinal_SNo with
x0.
The subproof is completed by applying H0.
Apply ordinal_SNo with
x1.
The subproof is completed by applying H1.
Apply ordinal_SNo with
x0.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Apply ordinal_In_SNoLt with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.
Assume H3: x0 ⊆ x1.
The subproof is completed by applying H3.