Theorem s4s4

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

	Ref	Expression
Assertion	s4s4	$$⊢⟨“ABCDEFGH”⟩=⟨“ABCD”⟩\mathrm{++}⟨“EFGH”⟩$$

Proof

Step	Hyp	Ref	Expression
1		df-s4	$$⊢⟨“EFGH”⟩=⟨“EFG”⟩\mathrm{++}⟨“H”⟩$$
2		s4cli	$$⊢⟨“ABCD”⟩\in \mathrm{Word}\mathrm{V}$$
3		s3cli	$$⊢⟨“EFG”⟩\in \mathrm{Word}\mathrm{V}$$
4		df-s8	$$⊢⟨“ABCDEFGH”⟩=⟨“ABCDEFG”⟩\mathrm{++}⟨“H”⟩$$
5		s4s3	$$⊢⟨“ABCDEFG”⟩=⟨“ABCD”⟩\mathrm{++}⟨“EFG”⟩$$
6	1 2 3 4 5	cats1cat	$$⊢⟨“ABCDEFGH”⟩=⟨“ABCD”⟩\mathrm{++}⟨“EFGH”⟩$$