Theorem unique_int_in_radius_one_open_interval of type Forall

from the theory of proveit.numbers.number_sets.real_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.real_numbers import unique_int_in_radius_one_open_interval

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

Passed sanity check: unique_int_in_radius_one_open_interval matches stored_expr

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

\forall_{a, b \in \mathbb{R}^+~|~a \leq 1, b \leq 1}~\left[\forall_{x \in \mathbb{Z}}~\left(\left(\left(x - a,x + b\right) \cap \mathbb{Z}\right) = \left\{x\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	50, 47
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, 14, 15
11	Lambda	parameter: 46 body: 16
12	Operation	operator: 28 operands: 17
13	Operation	operator: 28 operands: 18
14	Operation	operator: 20 operands: 19
15	Operation	operator: 20 operands: 21
16	Conditional	value: 22 condition: 23
17	ExprTuple	50, 24
18	ExprTuple	47, 24
19	ExprTuple	50, 25
20	Literal
21	ExprTuple	47, 25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operands: 29
24	Literal
25	Literal
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	46, 37
30	Operation	operator: 32 operands: 33
31	Operation	operator: 34 operand: 46
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	46
36	Operation	operator: 38 operands: 39
37	Literal
38	Literal
39	ExprTuple	40, 41
40	Operation	operator: 43 operands: 42
41	Operation	operator: 43 operands: 44
42	ExprTuple	46, 45
43	Literal
44	ExprTuple	46, 47
45	Operation	operator: 48 operand: 50
46	Variable
47	Variable
48	Literal
49	ExprTuple	50
50	Variable