Expression of type Forall

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 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, NaturalPos, frac, zero

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [m, n], instance_expr = 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)), domain = 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())

\forall_{m, n \in \mathbb{N}^+}~\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)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	57, 60
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 22 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12
10	Lambda	parameters: 13 body: 14
11	Operation	operator: 49 operands: 15
12	Operation	operator: 49 operands: 16
13	ExprTuple	52, 53, 51, 54
14	Conditional	value: 17 condition: 18
15	ExprTuple	57, 19
16	ExprTuple	60, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27, 28, 29, 30
24	Operation	operator: 46 operands: 31
25	Operation	operator: 44 operands: 32
26	ExprRange	lambda_map: 33 start_index: 59 end_index: 57
27	Operation	operator: 49 operands: 34
28	Operation	operator: 49 operands: 35
29	ExprRange	lambda_map: 36 start_index: 59 end_index: 60
30	Operation	operator: 37 operands: 38
31	ExprTuple	52, 39, 54
32	ExprTuple	40, 51
33	Lambda	parameter: 66 body: 41
34	ExprTuple	53, 55
35	ExprTuple	51, 55
36	Lambda	parameter: 66 body: 42
37	Literal
38	ExprTuple	51, 43
39	Operation	operator: 44 operands: 45
40	Operation	operator: 46 operands: 47
41	Operation	operator: 49 operands: 48
42	Operation	operator: 49 operands: 50
43	Literal
44	Literal
45	ExprTuple	53, 51
46	Literal
47	ExprTuple	52, 53, 54
48	ExprTuple	61, 55
49	Literal
50	ExprTuple	62, 55
51	Variable
52	ExprRange	lambda_map: 56 start_index: 59 end_index: 57
53	Variable
54	ExprRange	lambda_map: 58 start_index: 59 end_index: 60
55	Literal
56	Lambda	parameter: 66 body: 61
57	Variable
58	Lambda	parameter: 66 body: 62
59	Literal
60	Variable
61	IndexedVar	variable: 63 index: 66
62	IndexedVar	variable: 64 index: 66
63	Variable
64	Variable
65	ExprTuple	66
66	Variable