Proof by induction enough for iff?

[tropic nimbus]

I proved the first statement with induction, but also need to prove a second statement using the first statement. To prove the second statement, I think the first would have to be bijective, but I'm not sure if I did that sufficiently.

The first statement proof starts at the "prove star." I am trying to show that if a<b then a^n<b^n for all a,b,n>0 using the field axioms.

The second proof starts under the line in the second image. I am trying to show that if a^k=b^k then a=b, also using only the field axioms.

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@tropic nimbus

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[tropic nimbus]

+close

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