Section some_properties_of_groups.
Variable E : Set.
Variable G : group E.
Let o := group_law G.
Let s := group_sym G.
Let e := group_neutral G.
Let assoc := group_assoc G.
Let l_neutral := group_l_neutral G.
Let r_neutral := group_r_neutral G.
Let l_sym := group_l_sym G.
Let r_sym := group_r_sym G.
Hint Resolve assoc l_sym l_neutral r_sym r_neutral.
Hint Unfold o s e.

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Lemma solve_equation : forall x y : E, o x y = e -> y = s x.