Metamath Proof Explorer

Theorem s1s3

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

Ref Expression
Assertion s1s3 
|- <" A B C D "> = ( <" A "> ++ <" B C D "> )

Proof

Step Hyp Ref Expression
1 df-s3 
 |-  <" B C D "> = ( <" B C "> ++ <" D "> )
2 s1cli 
 |-  <" A "> e. Word _V
3 s2cli 
 |-  <" B C "> e. Word _V
4 df-s4 
 |-  <" A B C D "> = ( <" A B C "> ++ <" D "> )
5 s1s2 
 |-  <" A B C "> = ( <" A "> ++ <" B C "> )
6 1 2 3 4 5 cats1cat 
 |-  <" A B C D "> = ( <" A "> ++ <" B C D "> )