Let x0 of type ι be given.
Let x1 of type ι be given.
Apply ordinal_trichotomy_or_impred with
x0,
x1,
TwoRamseyGraph_3_6_17 (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) ⟶ TwoRamseyGraph_3_6_17 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 unknownprop_5cece90b225888ed5e86060411031b7dea9c395004ca9e7ebb9069250f2769f8 with
x1,
x0.
Apply unknownprop_aaaaeba8fcdb27b9f83a6b70c52949fdb89ad7f44ebb4e9ad9a0831ceeb37dae with
x1,
x0 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Assume H2: x0 = x1.
Apply H2 with
λ x2 x3 . TwoRamseyGraph_3_6_17 x0 x2.
Apply unknownprop_5458e899756973167cd95c9099f5886372156be9a958a28ab2e574c5fe52f55b with
u17_to_Church17 x0.
Apply unknownprop_f44342ed74648c23c8734d945bc8b2c1af5a9cb594ef51477e7844cb71f944f8 with
x0.
Apply ordsuccI1 with
u16,
x0.
The subproof is completed by applying H0.
Assume H2: x1 ∈ x0.
Apply unknownprop_aaaaeba8fcdb27b9f83a6b70c52949fdb89ad7f44ebb4e9ad9a0831ceeb37dae with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.