Proof: Algebra 7

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	x / x = 1	if not (x = 0), then x / x = 1 (Multiplicative Inverse Property)
2	a ⋅ (x / x) = a ⋅ 1	if x / x = 1, then a ⋅ (x / x) = a ⋅ 1 (Multiplicative Property of Equality Variation 1)
3	a ⋅ 1 = a	a ⋅ 1 = a (Multiplicative Identity)
4	a ⋅ (x / x) = a	if a ⋅ 1 = a and a ⋅ (x / x) = a ⋅ 1, then a ⋅ (x / x) = a (Transitive Property of Equality)
5	a ⋅ (x / x) = (a ⋅ x) / x	a ⋅ (x / x) = (a ⋅ x) / x (division_is_commutative)
6	(a ⋅ x) / x = a	if a ⋅ (x / x) = a and a ⋅ (x / x) = (a ⋅ x) / x, then (a ⋅ x) / x = a (Transitive Property of Equality Variation 2)

Comments

Please log in to add comments