Theorem div_by_frac_is_mult_by_reciprocal 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 div_by_frac_is_mult_by_reciprocal

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

Passed sanity check: div_by_frac_is_mult_by_reciprocal matches stored_expr

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

\forall_{x, y, z \in \mathbb{C}~|~y \neq 0, z \neq 0}~\left(\frac{x}{\frac{y}{z}} = \left(x \cdot \frac{z}{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: 4 body: 5
4	ExprTuple	31, 38, 37
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
12	Operation	operator: 35 operands: 19
13	Operation	operator: 20 operands: 21
14	Operation	operator: 24 operands: 22
15	Operation	operator: 24 operands: 23
16	Operation	operator: 24 operands: 25
17	Operation	operator: 27 operands: 26
18	Operation	operator: 27 operands: 28
19	ExprTuple	31, 29
20	Literal
21	ExprTuple	31, 30
22	ExprTuple	31, 32
23	ExprTuple	38, 32
24	Literal
25	ExprTuple	37, 32
26	ExprTuple	38, 33
27	Literal
28	ExprTuple	37, 33
29	Operation	operator: 35 operands: 34
30	Operation	operator: 35 operands: 36
31	Variable
32	Literal
33	Literal
34	ExprTuple	38, 37
35	Literal
36	ExprTuple	37, 38
37	Variable
38	Variable