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

# build up the expression from sub-expressions
sub_expr1 = [y]
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(Py, Complex), domain = S), 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())

\left(\forall_{y \in S}~\left(P\left(y\right) \in \mathbb{C}\right), \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)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 4 operand: 6
2	Operation	operator: 4 operand: 7
3	ExprTuple	6
4	Literal
5	ExprTuple	7
6	Lambda	parameter: 48 body: 8
7	Lambda	parameter: 42 body: 10
8	Conditional	value: 11 condition: 40
9	ExprTuple	42
10	Conditional	value: 12 condition: 13
11	Operation	operator: 43 operands: 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	41, 30
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 38 operands: 23
20	Operation	operator: 32 operand: 29
21	Operation	operator: 43 operands: 25
22	Operation	operator: 26 operands: 27
23	ExprTuple	28, 42
24	ExprTuple	29
25	ExprTuple	42, 30
26	Literal
27	ExprTuple	42, 31
28	Operation	operator: 32 operand: 35
29	Lambda	parameter: 48 body: 34
30	Literal
31	Literal
32	Literal
33	ExprTuple	35
34	Conditional	value: 36 condition: 40
35	Lambda	parameter: 48 body: 37
36	Operation	operator: 38 operands: 39
37	Conditional	value: 41 condition: 40
38	Literal
39	ExprTuple	41, 42
40	Operation	operator: 43 operands: 44
41	Operation	operator: 45 operand: 48
42	Variable
43	Literal
44	ExprTuple	48, 47
45	Variable
46	ExprTuple	48
47	Variable
48	Variable