Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply unknownprop_10cfff1173259328ed05ac7e63c6e194463722e1152adf6ca3f775a31e4297bc with
λ x3 x4 : ι → ι → ι → ο . x4 x0 x1 x2 ⟶ ∀ x5 : ο . (∀ x6 x7 . equip (setsum x0 x6) x1 ⟶ equip (setprod x7 x6) x2 ⟶ x5) ⟶ (∀ x6 x7 . equip (setsum x1 x6) x0 ⟶ equip (setprod x7 x6) x2 ⟶ x5) ⟶ x5.
Let x3 of type ο be given.
Apply H0 with
x3.
Let x4 of type ι be given.
Apply H3 with
x3.
Let x5 of type ι be given.
Apply unknownprop_eb8e8f72a91f1b934993d4cb19c84c8270f73a3626f3022b683d960a7fef89cb with
and (equip (setsum x0 x4) x1) (equip (setprod x5 x4) x2),
and (equip (setsum x1 x4) x0) (equip (setprod x5 x4) x2),
x3 leaving 3 subgoals.
The subproof is completed by applying H4.
Apply andE with
equip (setsum x0 x4) x1,
equip (setprod x5 x4) x2,
x3 leaving 2 subgoals.
The subproof is completed by applying H5.
Apply H1 with
x4,
x5 leaving 2 subgoals.
The subproof is completed by applying H6.
The subproof is completed by applying H7.
Apply andE with
equip (setsum x1 x4) x0,
equip (setprod x5 x4) x2,
x3 leaving 2 subgoals.
The subproof is completed by applying H5.
Apply H2 with
x4,
x5 leaving 2 subgoals.
The subproof is completed by applying H6.
The subproof is completed by applying H7.