Expression of type ExprTuple

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, ExprTuple, IndexedVar, Lambda, 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 = ExprTuple(Lambda([w_1_to_m, x, y, z_1_to_n], 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(\left(w_{1}, w_{2}, \ldots, w_{m}, x, y, z_{1}, z_{2}, \ldots, z_{n}\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	44, 45, 38, 46
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14, 15, 16
10	Operation	operator: 31 operands: 17
11	Operation	operator: 40 operand: 26
12	ExprRange	lambda_map: 19 start_index: 50 end_index: 48
13	Operation	operator: 34 operands: 20
14	Operation	operator: 34 operands: 21
15	ExprRange	lambda_map: 22 start_index: 50 end_index: 51
16	Operation	operator: 23 operands: 24
17	ExprTuple	25, 38
18	ExprTuple	26
19	Lambda	parameter: 57 body: 27
20	ExprTuple	45, 39
21	ExprTuple	38, 39
22	Lambda	parameter: 57 body: 28
23	Literal
24	ExprTuple	38, 29
25	Operation	operator: 42 operands: 30
26	Operation	operator: 31 operands: 32
27	Operation	operator: 34 operands: 33
28	Operation	operator: 34 operands: 35
29	Literal
30	ExprTuple	44, 36, 46
31	Literal
32	ExprTuple	37, 38
33	ExprTuple	52, 39
34	Literal
35	ExprTuple	53, 39
36	Operation	operator: 40 operand: 45
37	Operation	operator: 42 operands: 43
38	Variable
39	Literal
40	Literal
41	ExprTuple	45
42	Literal
43	ExprTuple	44, 45, 46
44	ExprRange	lambda_map: 47 start_index: 50 end_index: 48
45	Variable
46	ExprRange	lambda_map: 49 start_index: 50 end_index: 51
47	Lambda	parameter: 57 body: 52
48	Variable
49	Lambda	parameter: 57 body: 53
50	Literal
51	Variable
52	IndexedVar	variable: 54 index: 57
53	IndexedVar	variable: 55 index: 57
54	Variable
55	Variable
56	ExprTuple	57
57	Variable