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, q
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Integer, Mod, Mult

# build up the expression from sub-expressions
expr = Conditional(Equals(a, Add(Mult(q, b), Mod(a, b))), InSet(q, Integer))

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\{a = \left(\left(q \cdot b\right) + \left(a ~\textup{mod}~ b\right)\right) \textrm{ if } q \in \mathbb{Z}\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	18, 7
5	Literal
6	ExprTuple	17, 8
7	Operation	operator: 9 operands: 10
8	Literal
9	Literal
10	ExprTuple	11, 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 19
15	Literal
16	ExprTuple	18, 19
17	Variable
18	Variable
19	Variable