let S be non empty partial quasi_total non-empty Group-like invariant TRSStr ; :: thesis: for a being Element of S st S is (R2) & S is (R4) holds
((a ") ") * (1. S) <<>> a
let a be Element of S; :: thesis: ( S is (R2) & S is (R4) implies ((a ") ") * (1. S) <<>> a )
assume A1: ( S is (R2) & S is (R4) ) ; :: thesis: ((a ") ") * (1. S) <<>> a
take ((a ") ") * ((a ") * a) ; :: according to ABSRED_0:def 20 :: thesis: ( ((a ") ") * (1. S) <=*= ((a ") ") * ((a ") * a) & ((a ") ") * ((a ") * a) =*=> a )
(a ") * a ==> 1. S by A1;
hence ((a ") ") * ((a ") * a) =*=> ((a ") ") * (1. S) by Th2, ThI3; :: thesis: ((a ") ") * ((a ") * a) =*=> a
thus ((a ") ") * ((a ") * a) =*=> a by A1, Th2; :: thesis: verum