(** * Proposition 22 Out of three straight lines, which are equal to three given straight lines, to construct a triangle: thus it is necessary that two of the straight lines taken together in any manner should be greater than the remaining one (cf. [I. 20]). *)
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(** This needs Circle/Circle intersection axiom *)

Lemma prop_22 : circle_circle -> forall A1 A2 B1 B2 C1 C2 A1' A2' B1' B2' C1' C2',
SumS A1 A2 B1 B2 C1' C2' -> SumS A1 A2 C1 C2 B1' B2' -> SumS B1 B2 C1 C2 A1' A2' ->
Le C1 C2 C1' C2' -> Le B1 B2 B1' B2' -> Le A1 A2 A1' A2' ->
exists F G K, Cong F G A1 A2 /\ Cong F K B1 B2 /\ Cong G K C1 C2.