Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι → ι → ο be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_6dcb04ae0478121c526d391ecd79d3bc0a122d2859e0d05240c64c5ef2e86108 with
dd3c8.. x0 x2 x4,
x1,
x3,
x5.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with
λ x6 x7 . x0 = x7.
The subproof is completed by applying unknownprop_80b971e1e769c036da944ad596d7d907ce651d9af374e9c7a1d04d6f88668c42 with x0, x2, x4.
Apply and3I with
x0 = x1,
∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x2 x6 x7 = x3 x6 x7,
x4 = x5 leaving 3 subgoals.
The subproof is completed by applying L2.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_99ef3c56c8cdbdbdd0c30f3ff13386c5db4ed206a6215787f09bd20975ed1342 with
x0,
x2,
x4,
x6,
x7,
λ x8 x9 : ο . x9 = x3 x6 x7 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply L2 with
λ x8 x9 . prim1 x6 x8.
The subproof is completed by applying H3.
Apply L2 with
λ x8 x9 . prim1 x7 x8.
The subproof is completed by applying H4.
Apply H0 with
λ x8 x9 . 2b2e3.. (f482f.. x9 (4ae4a.. 4a7ef..)) x6 x7 = x3 x6 x7.
Let x8 of type ο → ο → ο be given.
Apply unknownprop_99ef3c56c8cdbdbdd0c30f3ff13386c5db4ed206a6215787f09bd20975ed1342 with
x1,
x3,
x5,
x6,
x7,
λ x9 x10 : ο . x8 x10 x9 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Apply unknownprop_f1e6338dba9d8a4b13d4526138bc59bec058c063c6bea746ef372dfd89320783 with
x0,
x2,
x4,
λ x6 x7 . x7 = x5.
Apply H0 with
λ x6 x7 . f482f.. x7 (4ae4a.. (4ae4a.. 4a7ef..)) = x5.
Let x6 of type ι → ι → ο be given.
The subproof is completed by applying unknownprop_f1e6338dba9d8a4b13d4526138bc59bec058c063c6bea746ef372dfd89320783 with x1, x3, x5, λ x7 x8 . x6 x8 x7.