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, c
from proveit.logic import And, InSet, NotEquals
from proveit.numbers import Abs, Add, LessEq, Mod, ModAbs, Real, subtract, zero

# build up the expression from sub-expressions
expr = Conditional(LessEq(ModAbs(subtract(Mod(Add(b, a), c), b), c), Abs(a)), And(InSet(a, Real), InSet(b, Real), InSet(c, Real), NotEquals(c, 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|\left(\left(b + a\right) ~\textup{mod}~ c\right) - b\right|_{\textup{mod}\thinspace c} \leq \left|a\right| \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R} ,  c \in \mathbb{R} ,  c \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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11, 12
7	Operation	operator: 13 operands: 14
8	Operation	operator: 15 operand: 38
9	Operation	operator: 19 operands: 17
10	Operation	operator: 19 operands: 18
11	Operation	operator: 19 operands: 20
12	Operation	operator: 21 operands: 22
13	Literal
14	ExprTuple	23, 34
15	Literal
16	ExprTuple	38
17	ExprTuple	38, 24
18	ExprTuple	37, 24
19	Literal
20	ExprTuple	34, 24
21	Literal
22	ExprTuple	34, 25
23	Operation	operator: 35 operands: 26
24	Literal
25	Literal
26	ExprTuple	27, 28
27	Operation	operator: 29 operands: 30
28	Operation	operator: 31 operand: 37
29	Literal
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	37
33	Operation	operator: 35 operands: 36
34	Variable
35	Literal
36	ExprTuple	37, 38
37	Variable
38	Variable