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, Equals, InSet
from proveit.numbers import Min, Mod, ModAbs, Neg, Real, RealPos

# build up the expression from sub-expressions
expr = Conditional(Equals(ModAbs(a, b), Min(Mod(a, b), Mod(Neg(a), b))), And(InSet(a, Real), InSet(b, 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\right|_{\textup{mod}\thinspace b} = {\rm Min}\left(a ~\textup{mod}~ b, \left(-a\right) ~\textup{mod}~ b\right) \textrm{ if } a \in \mathbb{R} ,  b \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
7	Operation	operator: 11 operands: 21
8	Operation	operator: 12 operands: 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	Literal
12	Literal
13	ExprTuple	17, 18
14	ExprTuple	28, 19
15	Literal
16	ExprTuple	25, 20
17	Operation	operator: 22 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	ExprTuple	28, 25
22	Literal
23	ExprTuple	24, 25
24	Operation	operator: 26 operand: 28
25	Variable
26	Literal
27	ExprTuple	28
28	Variable