∀ a b c, ((b + c) × a) = ((b × a) + (c × a))

Theorem distributive_times_plus_r : forall (a:nat), forall (b:nat), forall (c:nat), logic.eq (nat) (times (plus b c) a) (plus (times b a) (times c a)).

theorem distributive_times_plus_r : \forall (a:nat). \forall (b:nat). \forall (c:nat). (eq) (nat) ((times) ((plus) b c) a) ((plus) ((times) b a) ((times) c a)).

theorem distributive_times_plus_r : forall (a:nat.nat) , forall (b:nat.nat) , forall (c:nat.nat) , (((logic.eq_) (nat.nat)) ((((nat.times) ) ((((nat.plus) ) (b)) (c))) (a))) ((((nat.plus) ) ((((nat.times) ) (b)) (a))) ((((nat.times) ) (c)) (a))).

distributive_times_plus_r : LEMMA (FORALL(a:nat_sttfa.sttfa_nat):(FORALL(b:nat_sttfa.sttfa_nat):(FORALL(c:nat_sttfa.sttfa_nat):logic_sttfa_th.eq[nat_sttfa.sttfa_nat](nat_sttfa.times(nat_sttfa.plus(b)(c))(a))(nat_sttfa.plus(nat_sttfa.times(b)(a))(nat_sttfa.times(c)(a))))))

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