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 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 = 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())

\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)

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