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, ExprRange, IndexedVar, Variable, m, n, w, x, y, z
from proveit.core_expr_types import w_1_to_m, z_1_to_n
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Complex, Mult, Neg, frac, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(w, sub_expr1)
sub_expr3 = IndexedVar(z, sub_expr1)
expr = Conditional(Equals(frac(x, Mult(w_1_to_m, Neg(y), z_1_to_n)), Neg(frac(x, Mult(w_1_to_m, y, z_1_to_n)))), And(ExprRange(sub_expr1, InSet(sub_expr2, Complex), one, m), InSet(x, Complex), InSet(y, Complex), ExprRange(sub_expr1, InSet(sub_expr3, Complex), one, n), NotEquals(y, zero), ExprRange(sub_expr1, NotEquals(sub_expr2, zero), one, m), ExprRange(sub_expr1, NotEquals(sub_expr3, zero), one, n)))

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}{w_{1} \cdot  w_{2} \cdot  \ldots \cdot  w_{m} \cdot \left(-y\right)\cdot z_{1} \cdot  z_{2} \cdot  \ldots \cdot  z_{n}} = \left(-\frac{x}{w_{1} \cdot  w_{2} \cdot  \ldots \cdot  w_{m} \cdot y\cdot z_{1} \cdot  z_{2} \cdot  \ldots \cdot  z_{n}}\right) \textrm{ if } \left(w_{1} \in \mathbb{C}\right) ,  \left(w_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(w_{m} \in \mathbb{C}\right) ,  x \in \mathbb{C} ,  y \in \mathbb{C}, \left(z_{1} \in \mathbb{C}\right) ,  \left(z_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(z_{n} \in \mathbb{C}\right) ,  y \neq 0, \left(w_{1} \neq 0\right) ,  \left(w_{2} \neq 0\right) ,  \ldots ,  \left(w_{m} \neq 0\right), \left(z_{1} \neq 0\right) ,  \left(z_{2} \neq 0\right) ,  \ldots ,  \left(z_{n} \neq 0\right)\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, 13, 14, 15
7	Operation	operator: 32 operands: 16
8	Operation	operator: 45 operand: 26
9	ExprRange	lambda_map: 18 start_index: 55 end_index: 53
10	Operation	operator: 35 operands: 19
11	Operation	operator: 35 operands: 20
12	ExprRange	lambda_map: 21 start_index: 55 end_index: 56
13	Operation	operator: 38 operands: 22
14	ExprRange	lambda_map: 23 start_index: 55 end_index: 53
15	ExprRange	lambda_map: 24 start_index: 55 end_index: 56
16	ExprTuple	41, 25
17	ExprTuple	26
18	Lambda	parameter: 62 body: 27
19	ExprTuple	41, 43
20	ExprTuple	50, 43
21	Lambda	parameter: 62 body: 28
22	ExprTuple	50, 44
23	Lambda	parameter: 62 body: 29
24	Lambda	parameter: 62 body: 30
25	Operation	operator: 47 operands: 31
26	Operation	operator: 32 operands: 33
27	Operation	operator: 35 operands: 34
28	Operation	operator: 35 operands: 36
29	Operation	operator: 38 operands: 37
30	Operation	operator: 38 operands: 39
31	ExprTuple	49, 40, 51
32	Literal
33	ExprTuple	41, 42
34	ExprTuple	57, 43
35	Literal
36	ExprTuple	58, 43
37	ExprTuple	57, 44
38	Literal
39	ExprTuple	58, 44
40	Operation	operator: 45 operand: 50
41	Variable
42	Operation	operator: 47 operands: 48
43	Literal
44	Literal
45	Literal
46	ExprTuple	50
47	Literal
48	ExprTuple	49, 50, 51
49	ExprRange	lambda_map: 52 start_index: 55 end_index: 53
50	Variable
51	ExprRange	lambda_map: 54 start_index: 55 end_index: 56
52	Lambda	parameter: 62 body: 57
53	Variable
54	Lambda	parameter: 62 body: 58
55	Literal
56	Variable
57	IndexedVar	variable: 59 index: 62
58	IndexedVar	variable: 60 index: 62
59	Variable
60	Variable
61	ExprTuple	62
62	Variable