Expression of type Conditional

from the theory of proveit.numbers.division

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, w, x, y, z
from proveit.logic import And, Equals, InSet
from proveit.numbers import ComplexNonZero, Mult, frac

# build up the expression from sub-expressions
expr = Conditional(Equals(Mult(frac(x, z), frac(y, w)), frac(Mult(x, y), Mult(z, w))), And(InSet(z, ComplexNonZero), InSet(w, ComplexNonZero)))

expr:

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

Passed sanity check: expr matches stored_expr

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

\left\{\left(\frac{x}{z} \cdot \frac{y}{w}\right) = \frac{x \cdot y}{z \cdot w} \textrm{ if } z \in \mathbb{C}^{\neq 0} ,  w \in \mathbb{C}^{\neq 0}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 25 operands: 11
8	Operation	operator: 22 operands: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	16, 17
12	ExprTuple	18, 19
13	ExprTuple	29, 20
14	Literal
15	ExprTuple	30, 20
16	Operation	operator: 22 operands: 21
17	Operation	operator: 22 operands: 23
18	Operation	operator: 25 operands: 24
19	Operation	operator: 25 operands: 26
20	Literal
21	ExprTuple	27, 29
22	Literal
23	ExprTuple	28, 30
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	29, 30
27	Variable
28	Variable
29	Variable
30	Variable