Theorem s1s2

Description: Concatenation of fixed length strings. (Contributed by Mario Carneiro, 26-Feb-2016)

	Ref	Expression
Assertion	s1s2	$$⊢⟨“ABC”⟩=⟨“A”⟩\mathrm{++}⟨“BC”⟩$$

Proof

Step	Hyp	Ref	Expression
1		df-s2	$$⊢⟨“BC”⟩=⟨“B”⟩\mathrm{++}⟨“C”⟩$$
2		s1cli	$$⊢⟨“A”⟩\in \mathrm{Word}\mathrm{V}$$
3		s1cli	$$⊢⟨“B”⟩\in \mathrm{Word}\mathrm{V}$$
4		df-s3	$$⊢⟨“ABC”⟩=⟨“AB”⟩\mathrm{++}⟨“C”⟩$$
5		df-s2	$$⊢⟨“AB”⟩=⟨“A”⟩\mathrm{++}⟨“B”⟩$$
6	1 2 3 4 5	cats1cat	$$⊢⟨“ABC”⟩=⟨“A”⟩\mathrm{++}⟨“BC”⟩$$