Theorem s1s6

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

	Ref	Expression
Assertion	s1s6	$$⊢⟨“ABCDEFG”⟩=⟨“A”⟩\mathrm{++}⟨“BCDEFG”⟩$$

Proof

Step	Hyp	Ref	Expression
1		df-s6	$$⊢⟨“BCDEFG”⟩=⟨“BCDEF”⟩\mathrm{++}⟨“G”⟩$$
2		s1cli	$$⊢⟨“A”⟩\in \mathrm{Word}\mathrm{V}$$
3		s5cli	$$⊢⟨“BCDEF”⟩\in \mathrm{Word}\mathrm{V}$$
4		df-s7	$$⊢⟨“ABCDEFG”⟩=⟨“ABCDEF”⟩\mathrm{++}⟨“G”⟩$$
5		s1s5	$$⊢⟨“ABCDEF”⟩=⟨“A”⟩\mathrm{++}⟨“BCDEF”⟩$$
6	1 2 3 4 5	cats1cat	$$⊢⟨“ABCDEFG”⟩=⟨“A”⟩\mathrm{++}⟨“BCDEFG”⟩$$