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, InSet, NotEquals
from proveit.numbers import Complex, frac, subtract, zero

# build up the expression from sub-expressions
expr = Conditional(Equals(frac(subtract(x, y), z), subtract(frac(x, z), frac(y, z))), And(InSet(x, Complex), InSet(y, Complex), InSet(z, Complex), NotEquals(z, zero)))

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\{\frac{x - y}{z} = \left(\frac{x}{z} - \frac{y}{z}\right) \textrm{ if } x \in \mathbb{C} ,  y \in \mathbb{C} ,  z \in \mathbb{C} ,  z \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, 11, 12
7	Operation	operator: 35 operands: 13
8	Operation	operator: 26 operands: 14
9	Operation	operator: 17 operands: 15
10	Operation	operator: 17 operands: 16
11	Operation	operator: 17 operands: 18
12	Operation	operator: 19 operands: 20
13	ExprTuple	21, 38
14	ExprTuple	22, 23
15	ExprTuple	31, 24
16	ExprTuple	37, 24
17	Literal
18	ExprTuple	38, 24
19	Literal
20	ExprTuple	38, 25
21	Operation	operator: 26 operands: 27
22	Operation	operator: 35 operands: 28
23	Operation	operator: 33 operand: 32
24	Literal
25	Literal
26	Literal
27	ExprTuple	31, 30
28	ExprTuple	31, 38
29	ExprTuple	32
30	Operation	operator: 33 operand: 37
31	Variable
32	Operation	operator: 35 operands: 36
33	Literal
34	ExprTuple	37
35	Literal
36	ExprTuple	37, 38
37	Variable
38	Variable