Expression of type ExprTuple

from the theory of proveit.numbers.number_sets.rational_numbers

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 GCD, NaturalPos, RationalPos, frac, one

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(q, Conditional(Exists(instance_param_or_params = [a, b], instance_expr = And(Equals(q, frac(a, b)), Equals(GCD(a, b), one)), domain = NaturalPos), InSet(q, RationalPos))))

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(q \mapsto \left\{\exists_{a, b \in \mathbb{N}^+}~\left(\left(q = \frac{a}{b}\right) \land \left(gcd\left(a, b\right) = 1\right)\right) \textrm{ if } q \in \mathbb{Q}^+\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	parameter: 27 body: 3
2	ExprTuple	27
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 25 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	27, 10
9	Lambda	parameters: 34 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 22 operands: 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 25 operands: 24
20	Operation	operator: 25 operands: 26
21	ExprTuple	27, 28
22	Literal
23	ExprTuple	29, 30
24	ExprTuple	35, 31
25	Literal
26	ExprTuple	36, 31
27	Variable
28	Operation	operator: 32 operands: 34
29	Operation	operator: 33 operands: 34
30	Literal
31	Literal
32	Literal
33	Literal
34	ExprTuple	35, 36
35	Variable
36	Variable