Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H2: x2 ∈ x1.
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_Hered with
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply ordinal_SNo with
x2.
The subproof is completed by applying L5.
Apply add_SNo_com with
x0,
x2,
λ x3 x4 . x4 ∈ add_SNo x0 x1 leaving 3 subgoals.
The subproof is completed by applying L3.
The subproof is completed by applying L6.
Apply add_SNo_com with
x0,
x1,
λ x3 x4 . add_SNo x2 x0 ∈ x4 leaving 3 subgoals.
The subproof is completed by applying L3.
The subproof is completed by applying L4.
Apply add_SNo_ordinal_InL with
x1,
x0,
x2 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
The subproof is completed by applying H2.