Let x0 of type ι be given.
Let x1 of type ι → ο be given.
Let x2 of type ι → ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Assume H0:
nIn x3 (ReplSep x0 (λ x5 . x1 x5) (λ x5 . x2 x5)).
Claim L4: x3 = x2 x4
Apply unknownprop_b777a79c17f16cd28153af063df26a4626b11c1f1d4394d7f537c11837ab0962 with
x3 = x2 x4.
The subproof is completed by applying H3.
Apply unknownprop_8369708f37c0d20e10b6156293f1b207e835dfc563ff7fbfa059bf26c84ddb80 with
x3,
ReplSep x0 (λ x5 . x1 x5) (λ x5 . x2 x5) leaving 2 subgoals.
The subproof is completed by applying H0.
Apply L4 with
λ x5 x6 . In x6 (ReplSep x0 x1 x2).
Apply unknownprop_8d2d2cad5b49b3f5b663b34a4b05b87bd91c0d0340dcf2eab94b6803f88f2fd8 with
x0,
x1,
x2,
x4 leaving 2 subgoals.
Apply unknownprop_75b5762e65badae8f9531d40fddd332ff95b59f608d93c7a55f19f4fa5ef37d5 with
x4,
x0.
The subproof is completed by applying H1.
Apply unknownprop_b777a79c17f16cd28153af063df26a4626b11c1f1d4394d7f537c11837ab0962 with
x1 x4.
The subproof is completed by applying H2.