let S be non empty partial quasi_total non-empty Group-like invariant TRSStr ; :: thesis: for a being Element of S st S is (R6) & S is (R7) holds
a * (1. S) <<>> a
let a be Element of S; :: thesis: ( S is (R6) & S is (R7) implies a * (1. S) <<>> a )
assume A1: ( S is (R6) & S is (R7) ) ; :: thesis: a * (1. S) <<>> a
take ((a ") ") * (1. S) ; :: according to ABSRED_0:def 20 :: thesis: ( a * (1. S) <=*= ((a ") ") * (1. S) & ((a ") ") * (1. S) =*=> a )
thus ((a ") ") * (1. S) =*=> a * (1. S) by A1, Th2; :: thesis: ((a ") ") * (1. S) =*=> a
thus ((a ") ") * (1. S) =*=> a by A1, Th2; :: thesis: verum