Let's prove the following theorem:

x^{(m + 1)} = (x^m) ⋅ x

Proof Table

#	Claim	Reason
1	x^{(m + 1)} = (x^m) ⋅ (x¹)	x^{(m + 1)} = (x^m) ⋅ (x¹) (Power By M and N)
2	x¹ = x	x¹ = x (Power By 1)
3	(x^m) ⋅ (x¹) = (x^m) ⋅ x	if x¹ = x, then (x^m) ⋅ (x¹) = (x^m) ⋅ x (Substitution)
4	x^{(m + 1)} = (x^m) ⋅ x	if x^{(m + 1)} = (x^m) ⋅ (x¹) and (x^m) ⋅ (x¹) = (x^m) ⋅ x, then x^{(m + 1)} = (x^m) ⋅ x (Transitive Property of Equality)

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