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Example

We show

forall x in Z, y in Z: x+y = y+x.

Take arbitrary x₀ in Z,y₀ in Z. We have to show

x₀+y₀ = y₀+x₀.

We know

x₀+y₀ = (definition of +)

I(x₀ +_N y₀, x₁ +_N y₁) = (commutativity of +_N)

I(y₀ +_N x₀, y₁ +_N x₁) = (definition of +)

y₀+x₀.

Author: Wolfgang Schreiner
Last Modification: November 30, 1999

`x`₀+`y`₀	=	(definition of +)
I(`x`₀ +_N `y`₀, `x`₁ +_N `y`₁)	=	(commutativity of +_N)
I(`y`₀ +_N `x`₀, `y`₁ +_N `x`₁)	=	(definition of +)
`y`₀+`x`₀.