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 Py, S, y, z
from proveit.logic import Equals, Forall, NotEquals
from proveit.numbers import Complex, Sum, frac, zero

# build up the expression from sub-expressions
sub_expr1 = [y]
expr = Forall(instance_param_or_params = [z], instance_expr = Equals(frac(Sum(index_or_indices = sub_expr1, summand = Py, domain = S), z), Sum(index_or_indices = sub_expr1, summand = frac(Py, z), domain = S)), domain = Complex, condition = NotEquals(z, 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_{z \in \mathbb{C}~|~z \neq 0}~\left(\frac{\sum_{y \in S}~P\left(y\right)}{z} = \left[\sum_{y \in S}~\frac{P\left(y\right)}{z}\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	parameter: 35 body: 5
4	ExprTuple	35
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
12	Operation	operator: 31 operands: 16
13	Operation	operator: 25 operand: 22
14	Operation	operator: 36 operands: 18
15	Operation	operator: 19 operands: 20
16	ExprTuple	21, 35
17	ExprTuple	22
18	ExprTuple	35, 23
19	Literal
20	ExprTuple	35, 24
21	Operation	operator: 25 operand: 28
22	Lambda	parameter: 41 body: 27
23	Literal
24	Literal
25	Literal
26	ExprTuple	28
27	Conditional	value: 29 condition: 33
28	Lambda	parameter: 41 body: 30
29	Operation	operator: 31 operands: 32
30	Conditional	value: 34 condition: 33
31	Literal
32	ExprTuple	34, 35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operand: 41
35	Variable
36	Literal
37	ExprTuple	41, 40
38	Variable
39	ExprTuple	41
40	Variable
41	Variable