Expression of type Forall

from the theory of proveit.numbers.modular

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import N, x
from proveit.logic import And, Equals, Forall
from proveit.numbers import LessEq, ModAbs, Real, RealPos, frac, two, zero

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x, N], instance_expr = Equals(ModAbs(x, N), x), domains = [Real, RealPos], condition = And(LessEq(zero, x), LessEq(x, frac(N, two))).with_total_ordering_style())

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{x \in \mathbb{R}, N \in \mathbb{R}^+~|~0 \leq x \leq \frac{N}{2}}~\left(\left|x\right|_{\textup{mod}\thinspace N} = x\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 15 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 19 operands: 9
7	Literal
8	ExprTuple	10, 29
9	ExprTuple	11, 12, 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 17 operands: 16
12	Operation	operator: 17 operands: 18
13	Operation	operator: 19 operands: 20
14	Literal
15	ExprTuple	29, 33
16	ExprTuple	29, 21
17	Literal
18	ExprTuple	33, 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	Literal
23	Operation	operator: 26 operands: 25
24	Operation	operator: 26 operands: 27
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	29, 30
28	Literal
29	Variable
30	Operation	operator: 31 operands: 32
31	Literal
32	ExprTuple	33, 34
33	Variable
34	Literal