Expression of type Exists

from the theory of proveit.numbers.exponentiation

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
from proveit.logic import And, Equals, Exists
from proveit.numbers import Abs, GCD, NaturalPos, frac, one, sqrt, two

# build up the expression from sub-expressions
expr = Exists(instance_param_or_params = [a, b], instance_expr = And(Equals(Abs(sqrt(two)), frac(a, b)), Equals(GCD(a, b), one)), domain = NaturalPos)

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())

\exists_{a, b \in \mathbb{N}^+}~\left(\left(\left|\sqrt{2}\right| = \frac{a}{b}\right) \land \left(gcd\left(a, b\right) = 1\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: 27 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 8 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	ExprTuple	20, 21
15	Literal
16	ExprTuple	22, 36
17	ExprTuple	29, 23
18	Literal
19	ExprTuple	30, 23
20	Operation	operator: 24 operand: 28
21	Operation	operator: 34 operands: 27
22	Operation	operator: 26 operands: 27
23	Literal
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	29, 30
28	Operation	operator: 31 operands: 32
29	Variable
30	Variable
31	Literal
32	ExprTuple	37, 33
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37
36	Literal
37	Literal