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(*      Distributivity                                   *)
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Axiom
Fmult_Fplus_distr : forall r1 r2 r3 : F, r1 * (r2 + r3) = r1 * r2 + r1 * r3.
Hint Resolve Fmult_Fplus_distr: field_hints.

Lemma Fth : field_theory 0 1 Fplus Fmult Fminus Fopp Fdiv Finv (@eq F).
Add Field Ff : Fth.