Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ι be given.
Apply unknownprop_7aec93233696102c2436f4a8c96f0327308c9d3339e09de38f55e901e0baed22 with
987b2.. x0 x2,
x1,
x3.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with
λ x4 x5 . x0 = x5.
The subproof is completed by applying unknownprop_8674365f14b0285b3312b4875395e693d6df9b10fe9756f39519b30aacbeca91 with x0, x2.
Apply andI with
x0 = x1,
∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x2 x4 x5 = x3 x4 x5 leaving 2 subgoals.
The subproof is completed by applying L2.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply L2 with
λ x6 x7 . prim1 x4 x6.
The subproof is completed by applying H3.
Apply L2 with
λ x6 x7 . prim1 x5 x6.
The subproof is completed by applying H4.
Apply unknownprop_a59155e51c734938987e2b9ffb79da15884213566add9a57beb57783508c1eb2 with
x0,
x2,
x4,
x5,
λ x6 x7 . x7 = x3 x4 x5 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply H0 with
λ x6 x7 . e3162.. (f482f.. x7 (4ae4a.. 4a7ef..)) x4 x5 = x3 x4 x5.
Let x6 of type ι → ι → ο be given.
Apply unknownprop_a59155e51c734938987e2b9ffb79da15884213566add9a57beb57783508c1eb2 with
x1,
x3,
x4,
x5,
λ x7 x8 . x6 x8 x7 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.