Apply unknownprop_f23dde3020cfe827bdc4db0338b279dd2c0f6c90742a195a1a7a614475669076 with
λ x0 . ∀ x1 . In x1 x0 ⟶ Subq x1 x0 leaving 2 subgoals.
Let x0 of type ι be given.
Apply FalseE with
Subq x0 0.
Apply unknownprop_1cc88f7e87aaf8c5cee24b4a69ff535a81e7855c45a9fd971eec05ee4cc28f9c with
x0.
The subproof is completed by applying H0.
Let x0 of type ι be given.
Assume H1:
∀ x1 . In x1 x0 ⟶ Subq x1 x0.
Let x1 of type ι be given.
Apply unknownprop_84fe37a922385756a4e0826a593defb788cadbe4bdc9a7fe6b519ea49f509df5 with
x0,
x1,
Subq x1 (ordsucc x0) leaving 3 subgoals.
The subproof is completed by applying H2.
Apply unknownprop_16d2e0ac4e61f9d6f4710f68fd29bc0751fdb2a43ae4ee41dc39565d6502f8a7 with
x1,
x0,
ordsucc x0 leaving 2 subgoals.
Apply H1 with
x1.
The subproof is completed by applying H3.
The subproof is completed by applying unknownprop_b2bebb8105f29e822888ab2d4b10db11282fc91a7326e3993f508ffc07b3af08 with x0.
Assume H3: x1 = x0.
Apply H3 with
λ x2 x3 . Subq x3 (ordsucc x0).
The subproof is completed by applying unknownprop_b2bebb8105f29e822888ab2d4b10db11282fc91a7326e3993f508ffc07b3af08 with x0.