Unset Regular Subst Tactic.

Lemma characterization_of_collinearity :
forall O E E' S U1 U2
A AX AY B BX BY C CX CY
AXMBX AYMBY BXMCX BYMCY XProd YProd,
Cd O E S U1 U2 A AX AY -> Cd O E S U1 U2 B BX BY -> Cd O E S U1 U2 C CX CY ->
Diff O E E' AX BX AXMBX -> Diff O E E' AY BY AYMBY ->
Diff O E E' BX CX BXMCX -> Diff O E E' BY CY BYMCY ->
Prod O E E' AXMBX BYMCY XProd -> Prod O E E' AYMBY BXMCX YProd ->
(Col A B C <-> XProd = YProd).