Expression of type ExprTuple

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, ExprTuple, Lambda, 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 = ExprTuple(Lambda([a, b], 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(\left(a, b\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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