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, a, b
from proveit.logic import And, InSet, NotEquals
from proveit.numbers import Abs, Integer, Interval, ModAbs, one, subtract, zero

# build up the expression from sub-expressions
expr = Conditional(InSet(ModAbs(a, b), Interval(zero, subtract(Abs(b), one))), And(InSet(a, Integer), InSet(b, Integer), NotEquals(b, zero)))

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\right|_{\textup{mod}\thinspace b} \in \{0~\ldotp \ldotp~\left|b\right| - 1\} \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  b \neq 0\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: 16 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9, 10
6	Operation	operator: 11 operands: 12
7	Operation	operator: 13 operands: 14
8	Operation	operator: 16 operands: 15
9	Operation	operator: 16 operands: 17
10	Operation	operator: 18 operands: 19
11	Literal
12	ExprTuple	21, 32
13	Literal
14	ExprTuple	23, 20
15	ExprTuple	21, 22
16	Literal
17	ExprTuple	32, 22
18	Literal
19	ExprTuple	32, 23
20	Operation	operator: 24 operands: 25
21	Variable
22	Literal
23	Literal
24	Literal
25	ExprTuple	26, 27
26	Operation	operator: 28 operand: 32
27	Operation	operator: 30 operand: 33
28	Literal
29	ExprTuple	32
30	Literal
31	ExprTuple	33
32	Variable
33	Literal