Using two forms of provability:
- Identity Elimination/Transitivity
- AnaCon: Analytical Consequence
Below, "Larger(x,y)" means "x is larger than y", "Smaller(x,y)" means "x is smaller than y", and "SameSize(x,y)" means "x is the same size as y".
What would be the best way (makes more logical sense) to prove the following:
- Larger(b, c)
- Smaller(b, d)
- SameSize(d, e)
--> Larger(e, c) <-- this is what we are trying to prove
I have the following proofs:
Proof # 1
4) Smaller(b, e) AnaCon: 2, 3
5) Larger(e, b) AnaCon: 4
6) Larger(e, c) AnaCon: 5, 1
Proof # 2
4) Smaller(b, e) AnaCon: 2, 3
5) Larger(e, c) AnaCon: 4, 1
Proof # 3
4) Smaller(c, d) AnaCon: 1, 2
5) Larger(e, c) AnaCon: 4, 3