Proof: Inequality Problem

Let's prove the following theorem:

The inequality properties allow us to add -4 to both sides.

x + 4 - 4 = x

and

9 - 4 = 5

so

x > 5

Proof:

Proof Table

#	Claim	Reason
1	(x + 4) + (4 ⋅ (-1)) > 9 + (4 ⋅ (-1))	if x + 4 > 9, then (x + 4) + (4 ⋅ (-1)) > 9 + (4 ⋅ (-1)) (Inequality Greater Than)
2	9 + (4 ⋅ (-1)) = 5	9 + (4 ⋅ (-1)) = 5 (Fixed Value Statement)
3	(x + 4) + (4 ⋅ (-1)) = x	(x + 4) + (4 ⋅ (-1)) = x (simplify_4)
4	x > 5	if (x + 4) + (4 ⋅ (-1)) > 9 + (4 ⋅ (-1)) and (x + 4) + (4 ⋅ (-1)) = x and 9 + (4 ⋅ (-1)) = 5, then x > 5 (Double Inequality 2)

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