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(* Regarding R *)
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(* Specifications: *)
Lemma not_IZR_0 : forall a : Z, (IZR a <> 0)%R -> a <> 0.
Lemma sqr_inv : forall a b : Z, b <> 0 ->
(1 + IZR a * / IZR b * (IZR a * / IZR b) <> 0)%R.
Lemma Rdiv_ge_0 : forall a b : R, (a >= 0 -> b > 0 -> a / b >= 0)%R.
Lemma Rcross_prod : forall a b c d : R,
(b <> 0 -> d <> 0 -> a / b = c / d -> a * d = b * c)%R.