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 ExprTuple, Lambda, c, d, f, fj, g, gj, j, x
from proveit.logic import Equals, Forall
from proveit.numbers import Complex, Integer, Interval, Mult, Sum

# build up the expression from sub-expressions
sub_expr1 = [j]
sub_expr2 = Interval(c, d)
expr = ExprTuple(Lambda([f, g], Forall(instance_param_or_params = [x], instance_expr = Forall(instance_param_or_params = [c, d], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = Mult(Mult(x, gj), fj), domain = sub_expr2), Mult(x, Sum(index_or_indices = sub_expr1, summand = Mult(gj, fj), domain = sub_expr2))), domain = Integer), domain = Complex)))

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\right) \mapsto \left[\forall_{x \in \mathbb{C}}~\left[\forall_{c, d \in \mathbb{Z}}~\left(\left(\sum_{j = c}^{d} \left(\left(x \cdot g\left(j\right)\right) \cdot f\left(j\right)\right)\right) = \left(x \cdot \left(\sum_{j = c}^{d} \left(g\left(j\right) \cdot f\left(j\right)\right)\right)\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	53, 52
3	Operation	operator: 10 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 48 body: 7
6	ExprTuple	48
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 13
9	Operation	operator: 46 operands: 12
10	Literal
11	ExprTuple	13
12	ExprTuple	48, 14
13	Lambda	parameters: 56 body: 15
14	Literal
15	Conditional	value: 16 condition: 17
16	Operation	operator: 18 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 34 operand: 30
23	Operation	operator: 44 operands: 27
24	Operation	operator: 46 operands: 28
25	Operation	operator: 46 operands: 29
26	ExprTuple	30
27	ExprTuple	48, 31
28	ExprTuple	58, 32
29	ExprTuple	59, 32
30	Lambda	parameter: 57 body: 33
31	Operation	operator: 34 operand: 37
32	Literal
33	Conditional	value: 36 condition: 42
34	Literal
35	ExprTuple	37
36	Operation	operator: 44 operands: 38
37	Lambda	parameter: 57 body: 39
38	ExprTuple	40, 50
39	Conditional	value: 41 condition: 42
40	Operation	operator: 44 operands: 43
41	Operation	operator: 44 operands: 45
42	Operation	operator: 46 operands: 47
43	ExprTuple	48, 49
44	Literal
45	ExprTuple	49, 50
46	Literal
47	ExprTuple	57, 51
48	Variable
49	Operation	operator: 52 operand: 57
50	Operation	operator: 53 operand: 57
51	Operation	operator: 55 operands: 56
52	Variable
53	Variable
54	ExprTuple	57
55	Literal
56	ExprTuple	58, 59
57	Variable
58	Variable
59	Variable