Theorem s1s3

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

	Ref	Expression
Assertion	s1s3	$$⊢⟨“ABCD”⟩=⟨“A”⟩\mathrm{++}⟨“BCD”⟩$$

Proof

Step	Hyp	Ref	Expression
1		df-s3	$$⊢⟨“BCD”⟩=⟨“BC”⟩\mathrm{++}⟨“D”⟩$$
2		s1cli	$$⊢⟨“A”⟩\in \mathrm{Word}\mathrm{V}$$
3		s2cli	$$⊢⟨“BC”⟩\in \mathrm{Word}\mathrm{V}$$
4		df-s4	$$⊢⟨“ABCD”⟩=⟨“ABC”⟩\mathrm{++}⟨“D”⟩$$
5		s1s2	$$⊢⟨“ABC”⟩=⟨“A”⟩\mathrm{++}⟨“BC”⟩$$
6	1 2 3 4 5	cats1cat	$$⊢⟨“ABCD”⟩=⟨“A”⟩\mathrm{++}⟨“BCD”⟩$$