Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H0:
nIn x2 (Repl x0 (λ x4 . x1 x4)).
Claim L3: x2 = x1 x3
Apply unknownprop_b777a79c17f16cd28153af063df26a4626b11c1f1d4394d7f537c11837ab0962 with
x2 = x1 x3.
The subproof is completed by applying H2.
Apply unknownprop_75b5762e65badae8f9531d40fddd332ff95b59f608d93c7a55f19f4fa5ef37d5 with
x3,
x0.
The subproof is completed by applying H1.
Apply unknownprop_8369708f37c0d20e10b6156293f1b207e835dfc563ff7fbfa059bf26c84ddb80 with
x2,
Repl x0 (λ x4 . x1 x4) leaving 2 subgoals.
The subproof is completed by applying H0.
Apply L3 with
λ x4 x5 . In x5 (Repl x0 (λ x6 . x1 x6)).
Apply unknownprop_63c308b92260dbfca8c9530846e6836ba3e6be221cc8e80fd61db913e01bdacf with
x0,
x1,
x3.
The subproof is completed by applying L4.