Theorem reduced_nat_pos_ratio of type Forall

from the theory of proveit.numbers.number_sets.rational_numbers

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.numbers.number_sets.rational_numbers import reduced_nat_pos_ratio

# check that the built expression is the same as the stored expression
assert reduced_nat_pos_ratio.expr == stored_expr
assert reduced_nat_pos_ratio.expr._style_id == stored_expr._style_id
print("Passed sanity check: reduced_nat_pos_ratio matches stored_expr")

Passed sanity check: reduced_nat_pos_ratio matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{q \in \mathbb{Q}^+}~\left[\exists_{a, b \in \mathbb{N}^+}~\left(\left(q = \frac{a}{b}\right) \land \left(gcd\left(a, b\right) = 1\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	parameter: 29 body: 5
4	ExprTuple	29
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 11
7	Operation	operator: 27 operands: 10
8	Literal
9	ExprTuple	11
10	ExprTuple	29, 12
11	Lambda	parameters: 36 body: 13
12	Literal
13	Conditional	value: 14 condition: 15
14	Operation	operator: 17 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 24 operands: 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 27 operands: 26
22	Operation	operator: 27 operands: 28
23	ExprTuple	29, 30
24	Literal
25	ExprTuple	31, 32
26	ExprTuple	37, 33
27	Literal
28	ExprTuple	38, 33
29	Variable
30	Operation	operator: 34 operands: 36
31	Operation	operator: 35 operands: 36
32	Literal
33	Literal
34	Literal
35	Literal
36	ExprTuple	37, 38
37	Variable
38	Variable