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 Mod, Real, RealPos

# build up the expression from sub-expressions
sub_expr1 = Mod(a, b)
expr = Conditional(Equals(Mod(sub_expr1, b), sub_expr1), 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(\left(a ~\textup{mod}~ b\right) ~\textup{mod}~ b\right) = \left(a ~\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, 14
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 17 operands: 10
8	Operation	operator: 12 operands: 11
9	Operation	operator: 12 operands: 13
10	ExprTuple	14, 20
11	ExprTuple	19, 15
12	Literal
13	ExprTuple	20, 16
14	Operation	operator: 17 operands: 18
15	Literal
16	Literal
17	Literal
18	ExprTuple	19, 20
19	Variable
20	Variable