Theorem unique_int_in_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_interval

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

Passed sanity check: unique_int_in_interval matches stored_expr

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

\forall_{a \in \mathbb{R}^+, b \in \mathbb{R}^+, x \in \mathbb{Z}, y \in \mathbb{Z}~|~a \leq 1, b \leq 1}~\left(\left(y \in \left(x - a,x + b\right)\right) \Rightarrow \left(y = x\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: 4 body: 5
4	ExprTuple	48, 45, 44, 33
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15, 16, 17, 18, 19
12	Operation	operator: 26 operands: 20
13	Operation	operator: 21 operands: 22
14	Operation	operator: 26 operands: 23
15	Operation	operator: 26 operands: 24
16	Operation	operator: 26 operands: 25
17	Operation	operator: 26 operands: 27
18	Operation	operator: 29 operands: 28
19	Operation	operator: 29 operands: 30
20	ExprTuple	33, 31
21	Literal
22	ExprTuple	33, 44
23	ExprTuple	48, 32
24	ExprTuple	45, 32
25	ExprTuple	44, 34
26	Literal
27	ExprTuple	33, 34
28	ExprTuple	48, 35
29	Literal
30	ExprTuple	45, 35
31	Operation	operator: 36 operands: 37
32	Literal
33	Variable
34	Literal
35	Literal
36	Literal
37	ExprTuple	38, 39
38	Operation	operator: 41 operands: 40
39	Operation	operator: 41 operands: 42
40	ExprTuple	44, 43
41	Literal
42	ExprTuple	44, 45
43	Operation	operator: 46 operand: 48
44	Variable
45	Variable
46	Literal
47	ExprTuple	48
48	Variable