Description: A number is less than or equal to itself plus a nonnegative integer. (Contributed by NM, 10-Mar-2005)
Ref | Expression | ||
---|---|---|---|
Assertion | nn0addge2 | |- ( ( A e. RR /\ N e. NN0 ) -> A <_ ( N + A ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0re | |- ( N e. NN0 -> N e. RR ) |
|
2 | nn0ge0 | |- ( N e. NN0 -> 0 <_ N ) |
|
3 | 1 2 | jca | |- ( N e. NN0 -> ( N e. RR /\ 0 <_ N ) ) |
4 | addge02 | |- ( ( A e. RR /\ N e. RR ) -> ( 0 <_ N <-> A <_ ( N + A ) ) ) |
|
5 | 4 | biimp3a | |- ( ( A e. RR /\ N e. RR /\ 0 <_ N ) -> A <_ ( N + A ) ) |
6 | 5 | 3expb | |- ( ( A e. RR /\ ( N e. RR /\ 0 <_ N ) ) -> A <_ ( N + A ) ) |
7 | 3 6 | sylan2 | |- ( ( A e. RR /\ N e. NN0 ) -> A <_ ( N + A ) ) |