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}")
expr = Conditional(Equals(frac(Mult(w_1_to_m, Neg(x), z_1_to_n), y), Neg(frac(Mult(w_1_to_m, x, z_1_to_n), y))), And(ExprRange(sub_expr1, InSet(IndexedVar(w, sub_expr1), Complex), one, m), InSet(x, Complex), InSet(y, Complex), ExprRange(sub_expr1, InSet(IndexedVar(z, sub_expr1), Complex), one, n), NotEquals(y, 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{w_{1} \cdot  w_{2} \cdot  \ldots \cdot  w_{m} \cdot \left(-x\right)\cdot z_{1} \cdot  z_{2} \cdot  \ldots \cdot  z_{n}}{y} = \left(-\frac{w_{1} \cdot  w_{2} \cdot  \ldots \cdot  w_{m} \cdot x\cdot z_{1} \cdot  z_{2} \cdot  \ldots \cdot  z_{n}}{y}\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\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
7	Operation	operator: 28 operands: 14
8	Operation	operator: 37 operand: 23
9	ExprRange	lambda_map: 16 start_index: 47 end_index: 45
10	Operation	operator: 31 operands: 17
11	Operation	operator: 31 operands: 18
12	ExprRange	lambda_map: 19 start_index: 47 end_index: 48
13	Operation	operator: 20 operands: 21
14	ExprTuple	22, 35
15	ExprTuple	23
16	Lambda	parameter: 54 body: 24
17	ExprTuple	42, 36
18	ExprTuple	35, 36
19	Lambda	parameter: 54 body: 25
20	Literal
21	ExprTuple	35, 26
22	Operation	operator: 39 operands: 27
23	Operation	operator: 28 operands: 29
24	Operation	operator: 31 operands: 30
25	Operation	operator: 31 operands: 32
26	Literal
27	ExprTuple	41, 33, 43
28	Literal
29	ExprTuple	34, 35
30	ExprTuple	49, 36
31	Literal
32	ExprTuple	50, 36
33	Operation	operator: 37 operand: 42
34	Operation	operator: 39 operands: 40
35	Variable
36	Literal
37	Literal
38	ExprTuple	42
39	Literal
40	ExprTuple	41, 42, 43
41	ExprRange	lambda_map: 44 start_index: 47 end_index: 45
42	Variable
43	ExprRange	lambda_map: 46 start_index: 47 end_index: 48
44	Lambda	parameter: 54 body: 49
45	Variable
46	Lambda	parameter: 54 body: 50
47	Literal
48	Variable
49	IndexedVar	variable: 51 index: 54
50	IndexedVar	variable: 52 index: 54
51	Variable
52	Variable
53	ExprTuple	54
54	Variable