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, ExprTuple, Lambda, m, n, x, y
from proveit.core_expr_types import w_1_to_m, z_1_to_n
from proveit.logic import And, Equals, Forall, InSet, NotEquals
from proveit.numbers import Complex, Mult, NaturalPos, frac, zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([m, n], Conditional(Forall(instance_param_or_params = [w_1_to_m, x, y, z_1_to_n], instance_expr = 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)), domain = Complex, condition = NotEquals(y, zero)), And(InSet(m, NaturalPos), InSet(n, NaturalPos)))))

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(\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}\right) \textrm{ if } m \in \mathbb{N}^+ ,  n \in \mathbb{N}^+\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	56, 59
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 21 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 12 body: 13
10	Operation	operator: 48 operands: 14
11	Operation	operator: 48 operands: 15
12	ExprTuple	51, 52, 50, 53
13	Conditional	value: 16 condition: 17
14	ExprTuple	56, 18
15	ExprTuple	59, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26, 27, 28, 29
23	Operation	operator: 45 operands: 30
24	Operation	operator: 43 operands: 31
25	ExprRange	lambda_map: 32 start_index: 58 end_index: 56
26	Operation	operator: 48 operands: 33
27	Operation	operator: 48 operands: 34
28	ExprRange	lambda_map: 35 start_index: 58 end_index: 59
29	Operation	operator: 36 operands: 37
30	ExprTuple	51, 38, 53
31	ExprTuple	39, 50
32	Lambda	parameter: 65 body: 40
33	ExprTuple	52, 54
34	ExprTuple	50, 54
35	Lambda	parameter: 65 body: 41
36	Literal
37	ExprTuple	50, 42
38	Operation	operator: 43 operands: 44
39	Operation	operator: 45 operands: 46
40	Operation	operator: 48 operands: 47
41	Operation	operator: 48 operands: 49
42	Literal
43	Literal
44	ExprTuple	52, 50
45	Literal
46	ExprTuple	51, 52, 53
47	ExprTuple	60, 54
48	Literal
49	ExprTuple	61, 54
50	Variable
51	ExprRange	lambda_map: 55 start_index: 58 end_index: 56
52	Variable
53	ExprRange	lambda_map: 57 start_index: 58 end_index: 59
54	Literal
55	Lambda	parameter: 65 body: 60
56	Variable
57	Lambda	parameter: 65 body: 61
58	Literal
59	Variable
60	IndexedVar	variable: 62 index: 65
61	IndexedVar	variable: 63 index: 65
62	Variable
63	Variable
64	ExprTuple	65
65	Variable