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 And, Card, Equals, Forall, Implies, InSet, SetOfAll
from proveit.numbers import Complex, Sum

# build up the expression from sub-expressions
sub_expr1 = [y]
expr = ExprTuple(Lambda([f, g, R, S], Conditional(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))), And(Equals(SetOfAll(instance_param_or_params = sub_expr1, instance_element = gy, domain = S), R), Equals(Card(S), n), Equals(Card(R), n)))))

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