Multiplicative Property of Equality Variation 1
Distributive Property 4
Distribute Half
Transitive Property of Equality Variation 2
Multiplicative Property of Equality Variation 2
Transitive Property of Equality Variation 3
Division is Commutative
Commutative Property Example 2
Commutative Property Variation 1
Substitution 2
Substitution 8
Substitution Example 10
Half Half One

Proof: Distribute Half

Let's prove the following theorem:

(a ⋅ (1 / 2)) + (a ⋅ (1 / 2)) = a

Proof:

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Proof Table
# Claim Reason
1 (1 / 2) + (1 / 2) = 1 (1 / 2) + (1 / 2) = 1
2 a ⋅ ((1 / 2) + (1 / 2)) = a ⋅ 1 if (1 / 2) + (1 / 2) = 1, then a ⋅ ((1 / 2) + (1 / 2)) = a ⋅ 1
3 a ⋅ 1 = a a ⋅ 1 = a
4 a ⋅ ((1 / 2) + (1 / 2)) = a if a ⋅ ((1 / 2) + (1 / 2)) = a ⋅ 1 and a ⋅ 1 = a, then a ⋅ ((1 / 2) + (1 / 2)) = a
5 (a ⋅ (1 / 2)) + (a ⋅ (1 / 2)) = a ⋅ ((1 / 2) + (1 / 2)) (a ⋅ (1 / 2)) + (a ⋅ (1 / 2)) = a ⋅ ((1 / 2) + (1 / 2))
6 (a ⋅ (1 / 2)) + (a ⋅ (1 / 2)) = a if (a ⋅ (1 / 2)) + (a ⋅ (1 / 2)) = a ⋅ ((1 / 2) + (1 / 2)) and a ⋅ ((1 / 2) + (1 / 2)) = a, then (a ⋅ (1 / 2)) + (a ⋅ (1 / 2)) = a
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