Theorem s4s2

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

	Ref	Expression
Assertion	s4s2	$$⊢⟨“ABCDEF”⟩=⟨“ABCD”⟩\mathrm{++}⟨“EF”⟩$$

Proof

Step	Hyp	Ref	Expression
1		df-s2	$$⊢⟨“EF”⟩=⟨“E”⟩\mathrm{++}⟨“F”⟩$$
2		s4cli	$$⊢⟨“ABCD”⟩\in \mathrm{Word}\mathrm{V}$$
3		s1cli	$$⊢⟨“E”⟩\in \mathrm{Word}\mathrm{V}$$
4		df-s6	$$⊢⟨“ABCDEF”⟩=⟨“ABCDE”⟩\mathrm{++}⟨“F”⟩$$
5		df-s5	$$⊢⟨“ABCDE”⟩=⟨“ABCD”⟩\mathrm{++}⟨“E”⟩$$
6	1 2 3 4 5	cats1cat	$$⊢⟨“ABCDEF”⟩=⟨“ABCD”⟩\mathrm{++}⟨“EF”⟩$$