let a be positive heavy Real; :: thesis: for c being positive light Real
for b, d being positive Real st log (a,b) >= log (c,d) & a > b holds
c < d
let c be positive light Real; :: thesis: for b, d being positive Real st log (a,b) >= log (c,d) & a > b holds
c < d
let b, d be positive Real; :: thesis: ( log (a,b) >= log (c,d) & a > b implies c < d )
assume A2: ( log (a,b) >= log (c,d) & a > b ) ; :: thesis: c < d
then log (a,b) < 1 by AG1;
then log (c,d) < 1 by A2, XXREAL_0:2;
hence c < d by AM1; :: thesis: verum