DJ logic

DJ logic is an esolang based on logic and DJing. it has two “systems”(the first one is Zion Gate Dub and the second is Amen). they are collections of rules and logical statements. only one rule of a system can be viewed at a time.. that rule is the one at a index. the index for Zion Gate Dub os called 1 and the one for Amen is called 2. 1 and 2 increments every iteration

program/syntax

each program is a list of theorems seperated by newlines. on this line theres also a | symbol and a number then another | and a system name. the syntax is:

E y there exists atleast one number x where expression y is true for this x(in expression y the symbol # is replaced with x)
£ y ~ (E y)
~ x not x
= x y is x equal to y?
≠ x y ~ (= y x)
^ x y x and y
v x y x or y
< x y x less than y?
> x y ~ (< x y)
<_ v (< x y) (= x y)
>_ x y ~(<_ x y)
A y for all numbers x, y is true where ˚ stands for x
arithemetic: +-*/

arbitrary vars exist too which are any non used letters in the english alphabet. these are constants

the systems

Zion Gate Dub:

A ((^ (> ˚ a) (< ˚ b))
A (£ (≠ #+˚ 0-1))
£ (< #+c 0)