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(*                         Expansions                                        *)
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Lemma bracket_expand (x a b c d a1 b1: point) :
x = (a ∨ b) ∧ (c ∨ d) :> vect ->
('[x, a1, b1] =
(-(1)) * '[a, a1, b1] * '[b, c, d]  + '[b, a1, b1] * '[a, c, d])%f.