Prove $x<y \land z>0 \Rightarrow x\cdot z < y \cdot z$ for all$x,y,z\in \mathbb{K}$ is it possible to prove it like that: $\begin{gather*} x\cdot z < y\cdot z \quad | \cdot z^{-1} \\\ x\cdot \underbrace{(z \cdot z^{-...--prophetes.ai

Prove $x<y \land z>0 \Rightarrow x\cdot z < y \cdot z$ for all$x,y,z\in \mathbb{K}$ is it possible to prove it like that: $\begin{gather} x\cdot z < y\cdot z \quad | \cdot z^{-1} \\\ x\cdot \underbrace{(z \cdot z^{-1})}_{\overset{}=1} \overset{}< y \cdot \underbrace{(z \cdot z^{-1})}_{\overset{}=1} \\\ 1\cdot x \overset{}< 1\cdot y \\\ x \overset{}< y \quad \Box \end{gather} $ Thanks in advance!

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