Search for blocks/addresses/...

Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: ordinal x0.
Assume H1: ordinal x1.
Assume H2: x0x1.
Claim L3: x0ordsucc x1
Apply ordinal_In_Or_Subq with x0, x1, x0ordsucc x1 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Assume H3: x0x1.
Apply ordsuccI1 with x1, x0.
The subproof is completed by applying H3.
Assume H3: x1x0.
Claim L4: x0 = x1
Apply set_ext with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply L4 with λ x2 x3 . x3ordsucc x1.
The subproof is completed by applying ordsuccI2 with x1.
Claim L4: SNo x0
Apply ordinal_SNo with x0.
The subproof is completed by applying H0.
Claim L5: SNoLev x0 = x0
Apply ordinal_SNoLev with x0.
The subproof is completed by applying H0.
Apply ordinal_SNoLev_max_2 with x1, x0 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying L4.
Apply L5 with λ x2 x3 . x3ordsucc x1.
The subproof is completed by applying L3.