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 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 Equals, Forall, 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([m, n], Forall(instance_param_or_params = [w_1_to_m, x, y, z_1_to_n], instance_expr = 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)))), domain = Complex, conditions = [NotEquals(y, zero), ExprRange(sub_expr1, NotEquals(IndexedVar(w, sub_expr1), zero), one, m), ExprRange(sub_expr1, NotEquals(IndexedVar(z, sub_expr1), 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(\left(m, n\right) \mapsto \left[\forall_{w_{1}, w_{2}, \ldots, w_{m}, x, y, z_{1}, z_{2}, \ldots, z_{n} \in \mathbb{C}~|~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)}~\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)\right)\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	61, 64
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 7 body: 8
7	ExprTuple	57, 49, 58, 59
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18, 19, 20, 21, 22, 23
15	Operation	operator: 40 operands: 24
16	Operation	operator: 53 operand: 34
17	ExprRange	lambda_map: 26 start_index: 63 end_index: 61
18	Operation	operator: 43 operands: 27
19	Operation	operator: 43 operands: 28
20	ExprRange	lambda_map: 29 start_index: 63 end_index: 64
21	Operation	operator: 46 operands: 30
22	ExprRange	lambda_map: 31 start_index: 63 end_index: 61
23	ExprRange	lambda_map: 32 start_index: 63 end_index: 64
24	ExprTuple	49, 33
25	ExprTuple	34
26	Lambda	parameter: 70 body: 35
27	ExprTuple	49, 51
28	ExprTuple	58, 51
29	Lambda	parameter: 70 body: 36
30	ExprTuple	58, 52
31	Lambda	parameter: 70 body: 37
32	Lambda	parameter: 70 body: 38
33	Operation	operator: 55 operands: 39
34	Operation	operator: 40 operands: 41
35	Operation	operator: 43 operands: 42
36	Operation	operator: 43 operands: 44
37	Operation	operator: 46 operands: 45
38	Operation	operator: 46 operands: 47
39	ExprTuple	57, 48, 59
40	Literal
41	ExprTuple	49, 50
42	ExprTuple	65, 51
43	Literal
44	ExprTuple	66, 51
45	ExprTuple	65, 52
46	Literal
47	ExprTuple	66, 52
48	Operation	operator: 53 operand: 58
49	Variable
50	Operation	operator: 55 operands: 56
51	Literal
52	Literal
53	Literal
54	ExprTuple	58
55	Literal
56	ExprTuple	57, 58, 59
57	ExprRange	lambda_map: 60 start_index: 63 end_index: 61
58	Variable
59	ExprRange	lambda_map: 62 start_index: 63 end_index: 64
60	Lambda	parameter: 70 body: 65
61	Variable
62	Lambda	parameter: 70 body: 66
63	Literal
64	Variable
65	IndexedVar	variable: 67 index: 70
66	IndexedVar	variable: 68 index: 70
67	Variable
68	Variable
69	ExprTuple	70
70	Variable