Theorem abs_frac of type Forall

from the theory of proveit.numbers.absolute_value

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.absolute_value import abs_frac

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

Passed sanity check: abs_frac matches stored_expr

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

\forall_{a, b \in \mathbb{C}~|~b \neq 0}~\left(\left|\frac{a}{b}\right| = \frac{\left|a\right|}{\left|b\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: 29 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14, 15
11	Operation	operator: 31 operand: 23
12	Operation	operator: 28 operands: 17
13	Operation	operator: 19 operands: 18
14	Operation	operator: 19 operands: 20
15	Operation	operator: 21 operands: 22
16	ExprTuple	23
17	ExprTuple	24, 25
18	ExprTuple	33, 26
19	Literal
20	ExprTuple	34, 26
21	Literal
22	ExprTuple	34, 27
23	Operation	operator: 28 operands: 29
24	Operation	operator: 31 operand: 33
25	Operation	operator: 31 operand: 34
26	Literal
27	Literal
28	Literal
29	ExprTuple	33, 34
30	ExprTuple	33
31	Literal
32	ExprTuple	34
33	Variable
34	Variable