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, frac, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(Mult(w_1_to_m, frac(x, y), z_1_to_n), 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\{\left(w_{1} \cdot  w_{2} \cdot  \ldots \cdot  w_{m} \cdot \frac{x}{y}\cdot z_{1} \cdot  z_{2} \cdot  \ldots \cdot  z_{n}\right) = \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} \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: 29 operands: 14
8	Operation	operator: 27 operands: 15
9	ExprRange	lambda_map: 16 start_index: 42 end_index: 40
10	Operation	operator: 32 operands: 17
11	Operation	operator: 32 operands: 18
12	ExprRange	lambda_map: 19 start_index: 42 end_index: 43
13	Operation	operator: 20 operands: 21
14	ExprTuple	35, 22, 37
15	ExprTuple	23, 34
16	Lambda	parameter: 49 body: 24
17	ExprTuple	36, 38
18	ExprTuple	34, 38
19	Lambda	parameter: 49 body: 25
20	Literal
21	ExprTuple	34, 26
22	Operation	operator: 27 operands: 28
23	Operation	operator: 29 operands: 30
24	Operation	operator: 32 operands: 31
25	Operation	operator: 32 operands: 33
26	Literal
27	Literal
28	ExprTuple	36, 34
29	Literal
30	ExprTuple	35, 36, 37
31	ExprTuple	44, 38
32	Literal
33	ExprTuple	45, 38
34	Variable
35	ExprRange	lambda_map: 39 start_index: 42 end_index: 40
36	Variable
37	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
38	Literal
39	Lambda	parameter: 49 body: 44
40	Variable
41	Lambda	parameter: 49 body: 45
42	Literal
43	Variable
44	IndexedVar	variable: 46 index: 49
45	IndexedVar	variable: 47 index: 49
46	Variable
47	Variable
48	ExprTuple	49
49	Variable