Theorem s1s7

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

	Ref	Expression
Assertion	s1s7	$$⊢⟨“ABCDEFGH”⟩=⟨“A”⟩\mathrm{++}⟨“BCDEFGH”⟩$$

Proof

Step	Hyp	Ref	Expression
1		df-s7	$$⊢⟨“BCDEFGH”⟩=⟨“BCDEFG”⟩\mathrm{++}⟨“H”⟩$$
2		s1cli	$$⊢⟨“A”⟩\in \mathrm{Word}\mathrm{V}$$
3		s6cli	$$⊢⟨“BCDEFG”⟩\in \mathrm{Word}\mathrm{V}$$
4		df-s8	$$⊢⟨“ABCDEFGH”⟩=⟨“ABCDEFG”⟩\mathrm{++}⟨“H”⟩$$
5		s1s6	$$⊢⟨“ABCDEFG”⟩=⟨“A”⟩\mathrm{++}⟨“BCDEFG”⟩$$
6	1 2 3 4 5	cats1cat	$$⊢⟨“ABCDEFGH”⟩=⟨“A”⟩\mathrm{++}⟨“BCDEFGH”⟩$$