Theorem s4s3

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

	Ref	Expression
Assertion	s4s3	$$⊢⟨“ABCDEFG”⟩=⟨“ABCD”⟩\mathrm{++}⟨“EFG”⟩$$

Proof

Step	Hyp	Ref	Expression
1		df-s3	$$⊢⟨“EFG”⟩=⟨“EF”⟩\mathrm{++}⟨“G”⟩$$
2		s4cli	$$⊢⟨“ABCD”⟩\in \mathrm{Word}\mathrm{V}$$
3		s2cli	$$⊢⟨“EF”⟩\in \mathrm{Word}\mathrm{V}$$
4		df-s7	$$⊢⟨“ABCDEFG”⟩=⟨“ABCDEF”⟩\mathrm{++}⟨“G”⟩$$
5		s4s2	$$⊢⟨“ABCDEF”⟩=⟨“ABCD”⟩\mathrm{++}⟨“EF”⟩$$
6	1 2 3 4 5	cats1cat	$$⊢⟨“ABCDEFG”⟩=⟨“ABCD”⟩\mathrm{++}⟨“EFG”⟩$$