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

# build up the expression from sub-expressions
sub_expr1 = [y]
expr = ExprTuple(Lambda([P, S], Implies(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(\left(P, S\right) \mapsto \left(\left[\forall_{y \in S}~\left(P\left(y\right) \in \mathbb{C}\right)\right] \Rightarrow \left[\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]\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	50, 52
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 9 operand: 11
7	Operation	operator: 9 operand: 12
8	ExprTuple	11
9	Literal
10	ExprTuple	12
11	Lambda	parameter: 53 body: 13
12	Lambda	parameter: 47 body: 15
13	Conditional	value: 16 condition: 45
14	ExprTuple	47
15	Conditional	value: 17 condition: 18
16	Operation	operator: 48 operands: 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprTuple	46, 35
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27
24	Operation	operator: 43 operands: 28
25	Operation	operator: 37 operand: 34
26	Operation	operator: 48 operands: 30
27	Operation	operator: 31 operands: 32
28	ExprTuple	33, 47
29	ExprTuple	34
30	ExprTuple	47, 35
31	Literal
32	ExprTuple	47, 36
33	Operation	operator: 37 operand: 40
34	Lambda	parameter: 53 body: 39
35	Literal
36	Literal
37	Literal
38	ExprTuple	40
39	Conditional	value: 41 condition: 45
40	Lambda	parameter: 53 body: 42
41	Operation	operator: 43 operands: 44
42	Conditional	value: 46 condition: 45
43	Literal
44	ExprTuple	46, 47
45	Operation	operator: 48 operands: 49
46	Operation	operator: 50 operand: 53
47	Variable
48	Literal
49	ExprTuple	53, 52
50	Variable
51	ExprTuple	53
52	Variable
53	Variable