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.
Let x4 of type ι → ι → ο be given.
Let x5 of type ι → ι → ο be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_7ce356354aa36dcd139ca17bef55c746d5b4310e6c5ca9185ed4eefda2acbfda with
4d5a4.. x0 x2 x4 x6,
x1,
x3,
x5,
x7.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with
λ x8 x9 . x0 = x9.
The subproof is completed by applying unknownprop_42a095fe3b02ba45094f1e14a1ac5ada5d6d439811f9566f16b43b84348ab77f with x0, x2, x4, x6.
Apply and4I with
x0 = x1,
∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x2 x8 x9 = x3 x8 x9,
∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x5 x8 x9,
x6 = x7 leaving 4 subgoals.
The subproof is completed by applying L2.
Let x8 of type ι be given.
Let x9 of type ι be given.
Apply unknownprop_f06b0a67dd5bbbeac58fd338a725d744b2a4efcf8fe27966dfa1185aa34a901c with
x0,
x2,
x4,
x6,
x8,
x9,
λ x10 x11 . x11 = x3 x8 x9 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply L2 with
λ x10 x11 . prim1 x8 x10.
The subproof is completed by applying H3.
Apply L2 with
λ x10 x11 . prim1 x9 x10.
The subproof is completed by applying H4.
Apply H0 with
λ x10 x11 . e3162.. (f482f.. x11 (4ae4a.. 4a7ef..)) x8 x9 = x3 x8 x9.
Let x10 of type ι → ι → ο be given.
Apply unknownprop_f06b0a67dd5bbbeac58fd338a725d744b2a4efcf8fe27966dfa1185aa34a901c with
x1,
x3,
x5,
x7,
x8,
x9,
λ x11 x12 . x10 x12 x11 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Let x8 of type ι be given.
Let x9 of type ι be given.
Apply unknownprop_e57334b898c7a3e2da00fbb9975b5ba2aef7c7a09b0668a091b2dc60dedd57bf with
x0,
x2,
x4,
x6,
x8,
x9,
λ x10 x11 : ο . x11 = x5 x8 x9 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply L2 with
λ x10 x11 . prim1 x8 x10.
The subproof is completed by applying H3.
Apply L2 with
λ x10 x11 . prim1 x9 x10.
The subproof is completed by applying H4.
Apply H0 with
λ x10 x11 . 2b2e3.. (f482f.. x11 (4ae4a.. (4ae4a.. 4a7ef..))) x8 x9 = x5 x8 x9.
Let x10 of type ο → ο → ο be given.
Apply unknownprop_e57334b898c7a3e2da00fbb9975b5ba2aef7c7a09b0668a091b2dc60dedd57bf with
x1,
x3,
x5,
x7,
x8,
x9,
λ x11 x12 : ο . x10 x12 x11 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Apply unknownprop_c215c3321ba335d997a7897a6163689a168ec4bedb2b0c5d919146b523668141 with
x0,
x2,
x4,
x6,
λ x8 x9 . x9 = x7.
Apply H0 with
λ x8 x9 . f482f.. x9 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) = x7.
Let x8 of type ι → ι → ο be given.
The subproof is completed by applying unknownprop_c215c3321ba335d997a7897a6163689a168ec4bedb2b0c5d919146b523668141 with x1, x3, x5, x7, λ x9 x10 . x8 x10 x9.