Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_30912f2cca40a10142321c491284d8399f9fb6058ea49ef0a3ac5fa1be4efa52 with
x0.
The subproof is completed by applying H0.
Apply unknownprop_b0d5c07b58c35dec2d98b8c0aef5865d54317627a7a2b363b61462669e811c57 with
x0.
The subproof is completed by applying H0.
Apply unknownprop_5e27941980fd82e6bd970186ba0607de8244696a96acf12736011288a143d4ba with
x1,
x0,
099f3.. x1 x0 leaving 4 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_30912f2cca40a10142321c491284d8399f9fb6058ea49ef0a3ac5fa1be4efa52 with
x0.
The subproof is completed by applying H0.
Apply H5 with
099f3.. x1 x0 leaving 2 subgoals.
The subproof is completed by applying H6.
Assume H6: x1 = x0.
Apply FalseE with
099f3.. x1 x0.
Apply In_irref with
x0.
Apply L4 with
λ x2 x3 . prim1 x2 x0.
Apply H6 with
λ x2 x3 . prim1 (e4431.. x2) x0.
The subproof is completed by applying H2.
Apply FalseE with
099f3.. x1 x0.
Apply unknownprop_334a5a4dfd5441f12538cd3c70458238b05308c372afbd4cf94b09dd8e7afe85 with
x0,
x1,
False leaving 6 subgoals.
The subproof is completed by applying L3.
The subproof is completed by applying H1.
The subproof is completed by applying H5.
Let x2 of type ι be given.
Apply L4 with
λ x2 x3 . prim1 x3 (e4431.. x1) ⟶ SNoEq_ x3 x0 x1 ⟶ prim1 x3 x1 ⟶ False.
Apply FalseE with
SNoEq_ x0 x0 x1 ⟶ prim1 x0 x1 ⟶ False.
Apply unknownprop_f1a526a64fd91875cd825eea7f2e7776b7f0e7be5dcee74dc03af1d7886d1eb6 with
x0,
e4431.. x1 leaving 2 subgoals.
The subproof is completed by applying H6.
The subproof is completed by applying H2.