Theorem left_factor_divisibility of type Forall

from the theory of proveit.numbers.divisibility

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.divisibility import left_factor_divisibility

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

Passed sanity check: left_factor_divisibility matches stored_expr

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

\forall_{x \in \mathbb{C}, y \in \mathbb{Z}~|~x \neq 0}~\left(x \rvert \left(x \cdot y\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: 16 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	25, 11
9	Literal
10	ExprTuple	12, 13, 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	Operation	operator: 20 operands: 21
15	Literal
16	ExprTuple	25, 23
17	ExprTuple	25, 22
18	Literal
19	ExprTuple	23, 24
20	Literal
21	ExprTuple	25, 26
22	Literal
23	Variable
24	Literal
25	Variable
26	Literal