Question Number 215944 by mokys last updated on 22/Jan/25
$${if}\:{m},{n},{z}\:\in{N}\:{so}\:,\:{m}<{n}\:{and}\:{z}<{m}\:{then}\:{z}<{n}\:?\: \\ $$
Answered by MrGaster last updated on 22/Jan/25
$$\forall{m},{n},{z}\in\mathbb{N} \\ $$$${m}<{n\&x}<{m} \\ $$$$\Rightarrow{z}<{n} \\ $$
Commented by mokys last updated on 22/Jan/25
$${i}\:{want}\:{prove}\:{by}\:{steps} \\ $$
Commented by MrGaster last updated on 22/Jan/25
Let others solve this request later.
Answered by mehdee7396 last updated on 22/Jan/25
$${n}−{m}>\mathrm{0}\:\:\&\:\:{m}−{z}>\mathrm{0} \\ $$$$\Rightarrow\left({n}−{m}\right)+\left({m}−{z}\right)>\mathrm{0} \\ $$$$\Rightarrow{n}−{z}>\mathrm{0}\Rightarrow{n}>{z} \\ $$