Theorem s1s4

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

	Ref	Expression
Assertion	s1s4	$$⊢⟨“ABCDE”⟩=⟨“A”⟩\mathrm{++}⟨“BCDE”⟩$$

Proof

Step	Hyp	Ref	Expression
1		df-s4	$$⊢⟨“BCDE”⟩=⟨“BCD”⟩\mathrm{++}⟨“E”⟩$$
2		s1cli	$$⊢⟨“A”⟩\in \mathrm{Word}\mathrm{V}$$
3		s3cli	$$⊢⟨“BCD”⟩\in \mathrm{Word}\mathrm{V}$$
4		df-s5	$$⊢⟨“ABCDE”⟩=⟨“ABCD”⟩\mathrm{++}⟨“E”⟩$$
5		s1s3	$$⊢⟨“ABCD”⟩=⟨“A”⟩\mathrm{++}⟨“BCD”⟩$$
6	1 2 3 4 5	cats1cat	$$⊢⟨“ABCDE”⟩=⟨“A”⟩\mathrm{++}⟨“BCDE”⟩$$