# Complement constraints

**Syntax:**

- `x` is numeric variable constrained, `y`/`z` are other variables, `N`s are constants
- `y|N` means "a variable `y` or a constant"
- `X` is a set variable, `Y`/`Z` are other set variables, `s` are constants

**Numeric:**

- Equal (`x = y|N`)
- Less (`x < y|N`)
- Less or equal (`x <= y|N`)
- Greater (`x > y|N`)
- Greater or equal (`x >= y|N`)
- (Some range stuff, poss. including offset range) // Range stuff can be emulated as `x > 2 and x < 10` // Yeah, but what about multiple ranges? Using conditional variables and stuff would get annoying when it's such a common thing we'll need
- Addition (`x|N + y|N = z|N`)
- Subtraction (`x|N - y|N = z|N`)
- Multiplication (`x|N * y|N = z|N`)
- Division (`x|N / y|N = z|N`)
- Integer divison (`x|N // y|N = z|N`)
- Modulo (`x|N % y|N = z|N`)
- Power (`x|N ** y|N = z|N`) // unknown if we'll want to have this
- Constant polynomial (`0 = N * x|N ** N + N * x|N ** (N - 1) + ... + N * x|N + N`)
- (Modular ranges, however those will work)

**Multitype:**

- Number-is-set (`x = X`)

**Set:**

- Union (`X|s union Y|s = Z|s`)
- Intersection (`X|s intr Y|s = Z|s`)
- Difference (`X|s diff Y|s = Z|s`)
- Symmetric difference (`X|s symd Y|s = Z|s`)
- In (`y|Y|N|s in X|s`)
- Not in (`¬(y|Y|N|s in X|s)`)
- Size (`size(X|s) = y|N`)
- Subset (`X|s sub Y|s = Z|s`)
- Proper subset (`X|s psub Y|s = Z|s`)
- Superset (`X|s sup Y|s = Z|s`)
- Proper superset (`X|s psup Y|s = Z|s`)
- Complement (`comp(x|s) = Y|s`)