Let x0 of type ι be given.
Let x1 of type ι → ι → ο be given.
Assume H0: ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ⟶ x1 x3 x2.
Let x2 of type ι be given.
Assume H3: x2 ∈ x0.
Let x3 of type ι be given.
Apply H5 with
5bab1.. x0 x1 leaving 8 subgoals.
Apply unknownprop_a4faad2bc838cc7f29f2b73a017b51405895bba23aa738f96583faa4a837d4c5 with
x0,
x1,
x2,
x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_e18744c3d33bc4ef873867d7f98e98e25e9dd0ab0bb48a2523925318511bea9c with
x0,
x1,
x2,
x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_444ac5296d62699c191ecde1c9ff568a53be57aa76c70772e6c0062c5482461e with
x0,
x1,
x2,
x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_771b2ed39f7e3adaca6bfd716c6dc6c9d20a4af7a3a9ec942cc4cac52a2691f4 with
x0,
x1,
x2,
x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_980ded8cbfc1b90a4fe56940f1963d452ec52fb2102e5e1b85b8e4c30764bc41 with
x0,
x1,
x2,
x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_037384acb30036c934f06f7a92ae6d84f5676a647a832b7610848bdebeb473bd with
x0,
x1,
x2,
x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_922badde7d127dd751d45f7764bdc6704a9db5790f19f053bd2c112758cd9b00 with
x0,
x1,
x2,
x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_cabc3cf98a7ef1f75531c3aae51178d8c90ad4ee44698c68d3bd26d488c89dd5 with
x0,
x1,
x2,
x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.