Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Open Scope nat_scope.
Definition sum_of_two_square :=
[qualify a x |
[exists a : 'I_x.+1, exists b : 'I_x.+1, x == a ^ 2 + b ^ 2]].
Fact sum2s0 : 0 \is a sum_of_two_square.

Lemma sum2sM_coprime x y :
coprime x y ->
x * y \is  a sum_of_two_square ->  x \is  a sum_of_two_square.