Theorem s2s2

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

	Ref	Expression
Assertion	s2s2	$$⊢⟨“ABCD”⟩=⟨“AB”⟩\mathrm{++}⟨“CD”⟩$$

Proof

Step	Hyp	Ref	Expression
1		df-s2	$$⊢⟨“CD”⟩=⟨“C”⟩\mathrm{++}⟨“D”⟩$$
2		s2cli	$$⊢⟨“AB”⟩\in \mathrm{Word}\mathrm{V}$$
3		s1cli	$$⊢⟨“C”⟩\in \mathrm{Word}\mathrm{V}$$
4		df-s4	$$⊢⟨“ABCD”⟩=⟨“ABC”⟩\mathrm{++}⟨“D”⟩$$
5		df-s3	$$⊢⟨“ABC”⟩=⟨“AB”⟩\mathrm{++}⟨“C”⟩$$
6	1 2 3 4 5	cats1cat	$$⊢⟨“ABCD”⟩=⟨“AB”⟩\mathrm{++}⟨“CD”⟩$$