Theorem complete_interval_left_shift_image_size of type Forall

from the theory of proveit.numbers.modular

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.modular import complete_interval_left_shift_image_size

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

Passed sanity check: complete_interval_left_shift_image_size matches stored_expr

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

\forall_{N \in \mathbb{N}^+}~\left[\forall_{a, b, c \in \mathbb{Z}~|~|\{a~\ldotp \ldotp~b\}| \geq N}~\left(|\left\{\left(c + x\right) ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}}| = N\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	parameter: 48 body: 4
3	ExprTuple	48
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 45 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	48, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	56, 57, 54
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20, 48
18	Literal
19	ExprTuple	21, 22, 23, 24
20	Operation	operator: 36 operand: 31
21	Operation	operator: 45 operands: 26
22	Operation	operator: 45 operands: 27
23	Operation	operator: 45 operands: 28
24	Operation	operator: 29 operands: 30
25	ExprTuple	31
26	ExprTuple	56, 32
27	ExprTuple	57, 32
28	ExprTuple	54, 32
29	Literal
30	ExprTuple	48, 33
31	Operation	operator: 34 operand: 38
32	Literal
33	Operation	operator: 36 operand: 49
34	Literal
35	ExprTuple	38
36	Literal
37	ExprTuple	49
38	Lambda	parameter: 55 body: 40
39	ExprTuple	55
40	Conditional	value: 41 condition: 42
41	Operation	operator: 43 operands: 44
42	Operation	operator: 45 operands: 46
43	Literal
44	ExprTuple	47, 48
45	Literal
46	ExprTuple	55, 49
47	Operation	operator: 50 operands: 51
48	Variable
49	Operation	operator: 52 operands: 53
50	Literal
51	ExprTuple	54, 55
52	Literal
53	ExprTuple	56, 57
54	Variable
55	Variable
56	Variable
57	Variable