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: Half Half One

Let's prove the following theorem:

((a ⋅ 1) / 2) + ((a ⋅ 1) / 2) = a

Proof:

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