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, 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 = [y], instance_expr = Equals(frac(Mult(y, x), Mult(z, x)), frac(y, z)), domain = Complex), And(InSet(x, ComplexNonZero), InSet(z, 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\{\forall_{y \in \mathbb{C}}~\left(\frac{y \cdot x}{z \cdot x} = \frac{y}{z}\right) \textrm{ if } x \in \mathbb{C}^{\neq 0} ,  z \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 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 32 body: 11
8	Operation	operator: 19 operands: 12
9	Operation	operator: 19 operands: 13
10	ExprTuple	32
11	Conditional	value: 14 condition: 15
12	ExprTuple	34, 16
13	ExprTuple	33, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Literal
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	32, 23
21	Operation	operator: 25 operands: 24
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	32, 33
27	Operation	operator: 30 operands: 29
28	Operation	operator: 30 operands: 31
29	ExprTuple	32, 34
30	Literal
31	ExprTuple	33, 34
32	Variable
33	Variable
34	Variable