Expression of type ExprTuple

from the theory of proveit.numbers.summation

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 Conditional, ExprTuple, Function, Lambda, R, S, a, f, fa, fx, g, gy, n, x, y
from proveit.logic import Card, Equals, Forall, Implies, InSet, SetOfAll
from proveit.numbers import Complex, Natural, Sum

# build up the expression from sub-expressions
sub_expr1 = [y]
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [f, g, R, S], instance_expr = Implies(Forall(instance_param_or_params = [a], instance_expr = InSet(fa, Complex), domain = R), Equals(Sum(index_or_indices = [x], summand = fx, domain = R), Sum(index_or_indices = sub_expr1, summand = Function(f, [gy]), domain = S))), conditions = [Equals(SetOfAll(instance_param_or_params = sub_expr1, instance_element = gy, domain = S), R), Equals(Card(S), n), Equals(Card(R), n)]), InSet(n, Natural))))

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(n \mapsto \left\{\forall_{f, g, R, S~|~\left\{g\left(y\right)\right\}_{y \in S} = R, |S| = n, |R| = n}~\left(\left[\forall_{a \in R}~\left(f\left(a\right) \in \mathbb{C}\right)\right] \Rightarrow \left(\left[\sum_{x \in R}~f\left(x\right)\right] = \left[\sum_{y \in S}~f\left(g\left(y\right)\right)\right]\right)\right) \textrm{ if } n \in \mathbb{N}\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	parameter: 36 body: 3
2	ExprTuple	36
3	Conditional	value: 4 condition: 5
4	Operation	operator: 23 operand: 8
5	Operation	operator: 67 operands: 7
6	ExprTuple	8
7	ExprTuple	36, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	65, 74, 71, 73
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21, 22
18	Operation	operator: 23 operand: 30
19	Operation	operator: 28 operands: 25
20	Operation	operator: 28 operands: 26
21	Operation	operator: 28 operands: 27
22	Operation	operator: 28 operands: 29
23	Literal
24	ExprTuple	30
25	ExprTuple	31, 32
26	ExprTuple	33, 71
27	ExprTuple	34, 36
28	Literal
29	ExprTuple	35, 36
30	Lambda	parameter: 69 body: 37
31	Operation	operator: 39 operand: 48
32	Operation	operator: 39 operand: 49
33	Operation	operator: 41 operand: 50
34	Operation	operator: 44 operand: 73
35	Operation	operator: 44 operand: 71
36	Variable
37	Conditional	value: 46 condition: 47
38	ExprTuple	48
39	Literal
40	ExprTuple	49
41	Literal
42	ExprTuple	50
43	ExprTuple	73
44	Literal
45	ExprTuple	71
46	Operation	operator: 67 operands: 51
47	Operation	operator: 67 operands: 52
48	Lambda	parameter: 70 body: 53
49	Lambda	parameter: 76 body: 54
50	Lambda	parameter: 76 body: 55
51	ExprTuple	56, 57
52	ExprTuple	69, 71
53	Conditional	value: 58 condition: 59
54	Conditional	value: 60 condition: 61
55	Conditional	value: 72 condition: 61
56	Operation	operator: 65 operand: 69
57	Literal
58	Operation	operator: 65 operand: 70
59	Operation	operator: 67 operands: 64
60	Operation	operator: 65 operand: 72
61	Operation	operator: 67 operands: 68
62	ExprTuple	69
63	ExprTuple	70
64	ExprTuple	70, 71
65	Variable
66	ExprTuple	72
67	Literal
68	ExprTuple	76, 73
69	Variable
70	Variable
71	Variable
72	Operation	operator: 74 operand: 76
73	Variable
74	Variable
75	ExprTuple	76
76	Variable