Let x0 of type ι be given.
Apply unknownprop_219a5692ece616b4a88502d80a85b644180cde982b21251f92a23d11d1a5d022 with
setsum (ReplSep x0 (λ x1 . In (setsum 0 (ap x1 1)) x0) (λ x1 . ap x1 1)) (ReplSep x0 (λ x1 . In (setsum 1 (ap x1 1)) x0) (λ x1 . ap x1 1)),
x0 leaving 2 subgoals.
Let x1 of type ι be given.
Apply unknownprop_976b9ed71c1ec1f277c9c37a01879b51c2de3497fe82149802bec54f853970e6 with
ReplSep x0 (λ x2 . In (setsum 0 (ap x2 1)) x0) (λ x2 . ap x2 1),
ReplSep x0 (λ x2 . In (setsum 1 (ap x2 1)) x0) (λ x2 . ap x2 1),
x1,
λ x2 . In x2 x0 leaving 3 subgoals.
The subproof is completed by applying H1.
Let x2 of type ι be given.
Apply unknownprop_021a576837934491f6aaf936d4c5a9c68d45f2b77fcd13cc395cfdeec72f7dac with
x0,
λ x3 . In (setsum 0 (ap x3 1)) x0,
λ x3 . ap x3 1,
x2,
In (setsum 0 x2) x0 leaving 2 subgoals.
The subproof is completed by applying H2.
Let x3 of type ι be given.
Apply H5 with
λ x4 x5 . In (setsum 0 x5) x0.
The subproof is completed by applying H4.
Let x2 of type ι be given.
Apply unknownprop_021a576837934491f6aaf936d4c5a9c68d45f2b77fcd13cc395cfdeec72f7dac with
x0,
λ x3 . In (setsum 1 ...) ...,
...,
...,
... leaving 2 subgoals.
Apply L1 with
λ x1 x2 . setsum_p x1.
The subproof is completed by applying unknownprop_f61ccefc6bc57eb6c116b3bc3f27a552fe11c91770c4e9cfa989285bab91c3f5 with
ReplSep x0 (λ x1 . In (setsum 0 (ap x1 1)) x0) (λ x1 . ap x1 1),
ReplSep x0 (λ x1 . In (setsum 1 (ap x1 1)) x0) (λ x1 . ap x1 1).