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ker_sdprodm
: forall (gT rT : finGroupType) (H K G : {group gT})
(fH : {morphism H >-> rT}) (fK : {morphism K >-> rT})
(eqHK_G : H ><| K = G) (actf : {in H & K, morph_act 'J 'J fH fK}),
'ker (sdprodm eqHK_G actf) =
[set a * b^-1 | a in H, b in K & fH a == fK b]
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