Theorem frac_cancel_right of type Forall

from the theory of proveit.numbers.division

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.division import frac_cancel_right

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

Passed sanity check: frac_cancel_right matches stored_expr

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

\forall_{x, z \in \mathbb{C}^{\neq 0}}~\left[\forall_{y \in \mathbb{C}}~\left(\frac{y \cdot x}{z \cdot x} = \frac{y}{z}\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	38, 37
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
11	Lambda	parameter: 36 body: 15
12	Operation	operator: 23 operands: 16
13	Operation	operator: 23 operands: 17
14	ExprTuple	36
15	Conditional	value: 18 condition: 19
16	ExprTuple	38, 20
17	ExprTuple	37, 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	Literal
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	36, 27
25	Operation	operator: 29 operands: 28
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	36, 37
31	Operation	operator: 34 operands: 33
32	Operation	operator: 34 operands: 35
33	ExprTuple	36, 38
34	Literal
35	ExprTuple	37, 38
36	Variable
37	Variable
38	Variable