Expression of type Forall

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 a, b, q
from proveit.logic import Equals, Exists, Forall
from proveit.numbers import Add, Integer, Mod, Mult, Real, RealPos

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b], instance_expr = Exists(instance_param_or_params = [q], instance_expr = Equals(a, Add(Mult(q, b), Mod(a, b))), domain = Integer), domains = [Real, 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())

\forall_{a \in \mathbb{R}, b \in \mathbb{R}^+}~\left[\exists_{q \in \mathbb{Z}}~\left(a = \left(\left(q \cdot b\right) + \left(a ~\textup{mod}~ b\right)\right)\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 35 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	12, 13
11	Lambda	parameter: 36 body: 15
12	Operation	operator: 24 operands: 16
13	Operation	operator: 24 operands: 17
14	ExprTuple	36
15	Conditional	value: 18 condition: 19
16	ExprTuple	37, 20
17	ExprTuple	38, 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operands: 25
20	Literal
21	Literal
22	Literal
23	ExprTuple	37, 26
24	Literal
25	ExprTuple	36, 27
26	Operation	operator: 28 operands: 29
27	Literal
28	Literal
29	ExprTuple	30, 31
30	Operation	operator: 32 operands: 33
31	Operation	operator: 34 operands: 35
32	Literal
33	ExprTuple	36, 38
34	Literal
35	ExprTuple	37, 38
36	Variable
37	Variable
38	Variable