Word Proofs In Geometry

Question

Given this axiomatic system:

1) any letter can change to A

2) two C's in a row can change to B

3)any word (an entire string of letters) can be doubled.

Given: C

Prove: AACB

Answer 1

C <--- given

CC <--- doubles : property #3

CCCC <--- doubles again : property #3

CCC(C) <--- puts parenthesis around the C

CCCCC <--- doubles only the last letter C in parenthesis

AACCC <--- C changes to A : property 1

AAC(CC) <--- puts parenthesis around the last pair of C

AACB <-- two C's in a row change to B: property 2