Let x0 of type ι be given.
Let x1 of type ι be given.
Apply ordinal_trichotomy_or_impred with
x0,
x1,
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0 = u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x1 ⟶ x0 = x1 leaving 5 subgoals.
Apply nat_p_ordinal with
x0.
Apply nat_p_trans with
u16,
x0 leaving 2 subgoals.
The subproof is completed by applying nat_16.
The subproof is completed by applying H0.
Apply nat_p_ordinal with
x1.
Apply nat_p_trans with
u16,
x1 leaving 2 subgoals.
The subproof is completed by applying nat_16.
The subproof is completed by applying H1.
Assume H2: x0 ∈ x1.
Apply FalseE with
x0 = x1.
Apply unknownprop_c22d5c95e506e0caba5e138a4cd5a3e41270f12ef666b7d9e985517b802d71a4 with
x1,
x0 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Let x2 of type ι → ι → ο be given.
The subproof is completed by applying H3 with λ x3 x4 . x2 x4 x3.
Assume H2: x0 = x1.
The subproof is completed by applying H2.
Assume H2: x1 ∈ x0.
Apply FalseE with
x0 = x1.
Apply unknownprop_c22d5c95e506e0caba5e138a4cd5a3e41270f12ef666b7d9e985517b802d71a4 with
x0,
x1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H3.