Expression of type Conditional

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 Conditional, N, a, b
from proveit.logic import And, InSet
from proveit.numbers import ModAbs, Real, RealPos, greater_eq, subtract

# build up the expression from sub-expressions
expr = Conditional(greater_eq(ModAbs(subtract(a, b), N), subtract(ModAbs(a, N), ModAbs(b, N))), And(InSet(a, Real), InSet(b, Real), InSet(N, RealPos)))

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())

\left\{\left|a - b\right|_{\textup{mod}\thinspace N} \geq \left(\left|a\right|_{\textup{mod}\thinspace N} - \left|b\right|_{\textup{mod}\thinspace N}\right) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R} ,  N \in \mathbb{R}^+\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11
7	Operation	operator: 25 operands: 12
8	Operation	operator: 30 operands: 13
9	Operation	operator: 16 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	18, 19
13	ExprTuple	20, 34
14	ExprTuple	28, 21
15	ExprTuple	35, 21
16	Literal
17	ExprTuple	34, 22
18	Operation	operator: 30 operands: 23
19	Operation	operator: 32 operand: 27
20	Operation	operator: 25 operands: 26
21	Literal
22	Literal
23	ExprTuple	28, 34
24	ExprTuple	27
25	Literal
26	ExprTuple	28, 29
27	Operation	operator: 30 operands: 31
28	Variable
29	Operation	operator: 32 operand: 35
30	Literal
31	ExprTuple	35, 34
32	Literal
33	ExprTuple	35
34	Variable
35	Variable