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 ExprTuple, Lambda, m, n, x, y
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, zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([m, n], Forall(instance_param_or_params = [w_1_to_m, x, y, z_1_to_n], instance_expr = 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))), domain = Complex, condition = 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(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(\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)\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	53, 56
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 7 body: 8
7	ExprTuple	49, 50, 43, 51
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
15	Operation	operator: 36 operands: 22
16	Operation	operator: 45 operand: 31
17	ExprRange	lambda_map: 24 start_index: 55 end_index: 53
18	Operation	operator: 39 operands: 25
19	Operation	operator: 39 operands: 26
20	ExprRange	lambda_map: 27 start_index: 55 end_index: 56
21	Operation	operator: 28 operands: 29
22	ExprTuple	30, 43
23	ExprTuple	31
24	Lambda	parameter: 62 body: 32
25	ExprTuple	50, 44
26	ExprTuple	43, 44
27	Lambda	parameter: 62 body: 33
28	Literal
29	ExprTuple	43, 34
30	Operation	operator: 47 operands: 35
31	Operation	operator: 36 operands: 37
32	Operation	operator: 39 operands: 38
33	Operation	operator: 39 operands: 40
34	Literal
35	ExprTuple	49, 41, 51
36	Literal
37	ExprTuple	42, 43
38	ExprTuple	57, 44
39	Literal
40	ExprTuple	58, 44
41	Operation	operator: 45 operand: 50
42	Operation	operator: 47 operands: 48
43	Variable
44	Literal
45	Literal
46	ExprTuple	50
47	Literal
48	ExprTuple	49, 50, 51
49	ExprRange	lambda_map: 52 start_index: 55 end_index: 53
50	Variable
51	ExprRange	lambda_map: 54 start_index: 55 end_index: 56
52	Lambda	parameter: 62 body: 57
53	Variable
54	Lambda	parameter: 62 body: 58
55	Literal
56	Variable
57	IndexedVar	variable: 59 index: 62
58	IndexedVar	variable: 60 index: 62
59	Variable
60	Variable
61	ExprTuple	62
62	Variable