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 And, Equals, Exists, InSet
from proveit.numbers import Add, Integer, Mod, Mult, Real, RealPos

# build up the expression from sub-expressions
expr = Conditional(Exists(instance_param_or_params = [q], instance_expr = Equals(a, Add(Mult(q, b), Mod(a, b))), domain = Integer), 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\{\exists_{q \in \mathbb{Z}}~\left(a = \left(\left(q \cdot b\right) + \left(a ~\textup{mod}~ b\right)\right)\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 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 32 body: 11
8	Operation	operator: 20 operands: 12
9	Operation	operator: 20 operands: 13
10	ExprTuple	32
11	Conditional	value: 14 condition: 15
12	ExprTuple	33, 16
13	ExprTuple	34, 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operands: 21
16	Literal
17	Literal
18	Literal
19	ExprTuple	33, 22
20	Literal
21	ExprTuple	32, 23
22	Operation	operator: 24 operands: 25
23	Literal
24	Literal
25	ExprTuple	26, 27
26	Operation	operator: 28 operands: 29
27	Operation	operator: 30 operands: 31
28	Literal
29	ExprTuple	32, 34
30	Literal
31	ExprTuple	33, 34
32	Variable
33	Variable
34	Variable