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, 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(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))

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(\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)

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	40, 41, 39, 42
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: 34 operands: 19
13	Operation	operator: 32 operands: 20
14	ExprRange	lambda_map: 21 start_index: 47 end_index: 45
15	Operation	operator: 37 operands: 22
16	Operation	operator: 37 operands: 23
17	ExprRange	lambda_map: 24 start_index: 47 end_index: 48
18	Operation	operator: 25 operands: 26
19	ExprTuple	40, 27, 42
20	ExprTuple	28, 39
21	Lambda	parameter: 54 body: 29
22	ExprTuple	41, 43
23	ExprTuple	39, 43
24	Lambda	parameter: 54 body: 30
25	Literal
26	ExprTuple	39, 31
27	Operation	operator: 32 operands: 33
28	Operation	operator: 34 operands: 35
29	Operation	operator: 37 operands: 36
30	Operation	operator: 37 operands: 38
31	Literal
32	Literal
33	ExprTuple	41, 39
34	Literal
35	ExprTuple	40, 41, 42
36	ExprTuple	49, 43
37	Literal
38	ExprTuple	50, 43
39	Variable
40	ExprRange	lambda_map: 44 start_index: 47 end_index: 45
41	Variable
42	ExprRange	lambda_map: 46 start_index: 47 end_index: 48
43	Literal
44	Lambda	parameter: 54 body: 49
45	Variable
46	Lambda	parameter: 54 body: 50
47	Literal
48	Variable
49	IndexedVar	variable: 51 index: 54
50	IndexedVar	variable: 52 index: 54
51	Variable
52	Variable
53	ExprTuple	54
54	Variable