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: prim1 x1 x0.
Claim L2: ordinal (4ae4a.. x1)
Apply unknownprop_1f03c3e4cc230143731a84d6351b78522f6051d5113f644774435abf9cb5a984 with x1.
Apply ordinal_Hered with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply ordinal_trichotomy_or with x0, 4ae4a.. x1, or (prim1 (4ae4a.. x1) x0) (x0 = 4ae4a.. x1) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L2.
Assume H3: or (prim1 x0 (4ae4a.. x1)) (x0 = 4ae4a.. x1).
Apply H3 with or (prim1 (4ae4a.. x1) x0) (x0 = 4ae4a.. x1) leaving 2 subgoals.
Assume H4: prim1 x0 (4ae4a.. x1).
Apply FalseE with or (prim1 (4ae4a.. x1) x0) (x0 = 4ae4a.. x1).
Apply unknownprop_dec2978c0a72cebd51fcab0a380f03d4d80d1ccd8f826d378953148c305a60f0 with x1, x0, False leaving 3 subgoals.
The subproof is completed by applying H4.
Assume H5: prim1 x0 x1.
Apply unknownprop_f1a526a64fd91875cd825eea7f2e7776b7f0e7be5dcee74dc03af1d7886d1eb6 with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H5.
The subproof is completed by applying H1.
Assume H5: x0 = x1.
Apply In_irref with x0.
Apply H5 with λ x2 x3 . prim1 x3 x0.
The subproof is completed by applying H1.
Assume H4: x0 = 4ae4a.. x1.
Apply orIR with prim1 (4ae4a.. x1) x0, x0 = 4ae4a.. x1.
The subproof is completed by applying H4.
Assume H3: prim1 (4ae4a.. x1) x0.
Apply orIL with prim1 (4ae4a.. x1) x0, x0 = 4ae4a.. x1.
The subproof is completed by applying H3.