let nn9 be Element of NAT ; ( nn9 > 0 implies ( [\(log (2,nn9))/] is Element of NAT & (6 * ([\(log (2,nn9))/] + 1)) + 1 > 0 ) )
assume
nn9 > 0
; ( [\(log (2,nn9))/] is Element of NAT & (6 * ([\(log (2,nn9))/] + 1)) + 1 > 0 )
then A1:
nn9 >= 0 + 1
by NAT_1:13;
log (2,1) = 0
by POWER:51;
then
log (2,nn9) >= 0
by A1, PRE_FF:10;
then
[\(log (2,nn9))/] >= [\0/]
by PRE_FF:9;
then
[\(log (2,nn9))/] >= 0
;
then reconsider F = [\(log (2,nn9))/] as Element of NAT by INT_1:3;
F is Element of NAT
;
hence
[\(log (2,nn9))/] is Element of NAT
; (6 * ([\(log (2,nn9))/] + 1)) + 1 > 0
(6 * F) + (6 * 1) >= 0
;
hence
(6 * ([\(log (2,nn9))/] + 1)) + 1 > 0
; verum