Proof: Subtract Bit Example

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	bit [ 0, [ 1, [ ] ] ] minus bit 1 = [ 1, bit [ 1, [ ] ] minus bit 1 ]	bit [ 0, [ 1, [ ] ] ] minus bit 1 = [ 1, bit [ 1, [ ] ] minus bit 1 ] (Subtract by 1 (2))
2	bit [ 1, [ ] ] minus bit 1 = [ 0, [ ] ]	bit [ 1, [ ] ] minus bit 1 = [ 0, [ ] ] (Subtract by 1)
3	[ 1, bit [ 1, [ ] ] minus bit 1 ] = [ 1, [ 0, [ ] ] ]	if bit [ 1, [ ] ] minus bit 1 = [ 0, [ ] ], then [ 1, bit [ 1, [ ] ] minus bit 1 ] = [ 1, [ 0, [ ] ] ] (Substitution)
4	bit [ 0, [ 1, [ ] ] ] minus bit 1 = [ 1, [ 0, [ ] ] ]	if bit [ 0, [ 1, [ ] ] ] minus bit 1 = [ 1, bit [ 1, [ ] ] minus bit 1 ] and [ 1, bit [ 1, [ ] ] minus bit 1 ] = [ 1, [ 0, [ ] ] ], then bit [ 0, [ 1, [ ] ] ] minus bit 1 = [ 1, [ 0, [ ] ] ] (Transitive Property of Equality)

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