let S be non empty partial quasi_total non-empty Group-like invariant TRSStr ; :: thesis: for a being Element of S st S is (R8) & S is (R9) holds
((a ") ") * (1. S) =*=> a
let a be Element of S; :: thesis: ( S is (R8) & S is (R9) implies ((a ") ") * (1. S) =*=> a )
assume ( S is (R8) & S is (R9) ) ; :: thesis: ((a ") ") * (1. S) =*=> a
then ( ((a ") ") * (1. S) ==> (a ") " & (a ") " ==> a ) ;
hence ((a ") ") * (1. S) =*=> a by Lem3; :: thesis: verum