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# Less than or equal relation is transitive.

Prove that if and , then .

Proof.
By the transitivity of (Theorem I.17), we have that if and , then .
Then, if and we have by substitution.
If and , then by substitution.
If and , then by transitivity of the relation. Hence, by definition of .
Thus, in all cases and implies

### 2 comments

• Jay says:

Hey Rori, sorry i am not very familiar with latex code
i typed up an alternate soln in Lyx and cut and pasted its contents here.
Any ideas how to integrate the symbols?