Distributive Property 2
Commutative Property Variation 1
Substitution 2
Substitution 6
Distributive Property 3
Multiplicative Property of Equality Variation 1
Associative Property of Multiplication 2
Transitive Property of Equality Variation 2
Transitive Property Application 2
Substitution 10
Transitive Property of Equality Variation 1
Divide Both Sides
Multiplicative Property of Equality Variation 2
Transitive Property of Equality Variation 3
Division is Commutative
Associative Property
Substitution 12
Divide Simplify 2
Simplify 2
Simplify 3
Transitive 2

Proof: Simplify 3

Let's prove the following theorem:

((b ⋅ 2) + (a ⋅ 2)) / 2 = b + a

Proof:

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