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, Forall, InSet
from proveit.numbers import Complex, ComplexNonZero, Mult, frac

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [z, w], instance_expr = Equals(Mult(frac(x, z), frac(y, w)), frac(Mult(x, y), Mult(z, w))), domain = ComplexNonZero), And(InSet(x, Complex), InSet(y, Complex)))

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\{\forall_{z, w \in \mathbb{C}^{\neq 0}}~\left(\left(\frac{x}{z} \cdot \frac{y}{w}\right) = \frac{x \cdot y}{z \cdot w}\right) \textrm{ if } x \in \mathbb{C} ,  y \in \mathbb{C}\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 operand: 6
2	Operation	operator: 17 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 38 body: 9
7	Operation	operator: 26 operands: 10
8	Operation	operator: 26 operands: 11
9	Conditional	value: 12 condition: 13
10	ExprTuple	39, 14
11	ExprTuple	40, 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	Literal
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 37 operands: 23
20	Operation	operator: 34 operands: 24
21	Operation	operator: 26 operands: 25
22	Operation	operator: 26 operands: 27
23	ExprTuple	28, 29
24	ExprTuple	30, 31
25	ExprTuple	41, 32
26	Literal
27	ExprTuple	42, 32
28	Operation	operator: 34 operands: 33
29	Operation	operator: 34 operands: 35
30	Operation	operator: 37 operands: 36
31	Operation	operator: 37 operands: 38
32	Literal
33	ExprTuple	39, 41
34	Literal
35	ExprTuple	40, 42
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	41, 42
39	Variable
40	Variable
41	Variable
42	Variable