Theorem s1s5

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

	Ref	Expression
Assertion	s1s5	$$⊢⟨“ABCDEF”⟩=⟨“A”⟩\mathrm{++}⟨“BCDEF”⟩$$

Proof

Step	Hyp	Ref	Expression
1		df-s5	$$⊢⟨“BCDEF”⟩=⟨“BCDE”⟩\mathrm{++}⟨“F”⟩$$
2		s1cli	$$⊢⟨“A”⟩\in \mathrm{Word}\mathrm{V}$$
3		s4cli	$$⊢⟨“BCDE”⟩\in \mathrm{Word}\mathrm{V}$$
4		df-s6	$$⊢⟨“ABCDEF”⟩=⟨“ABCDE”⟩\mathrm{++}⟨“F”⟩$$
5		s1s4	$$⊢⟨“ABCDE”⟩=⟨“A”⟩\mathrm{++}⟨“BCDE”⟩$$
6	1 2 3 4 5	cats1cat	$$⊢⟨“ABCDEF”⟩=⟨“A”⟩\mathrm{++}⟨“BCDEF”⟩$$