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, Lambda, c, d, fj, gj, j, x
from proveit.logic import Equals, Forall, InSet
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(x, Conditional(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), InSet(x, 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(x \mapsto \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) \textrm{ if } x \in \mathbb{C}\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: 44 body: 3
2	ExprTuple	44
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 42 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	44, 10
9	Lambda	parameters: 52 body: 11
10	Literal
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
18	Operation	operator: 30 operand: 26
19	Operation	operator: 40 operands: 23
20	Operation	operator: 42 operands: 24
21	Operation	operator: 42 operands: 25
22	ExprTuple	26
23	ExprTuple	44, 27
24	ExprTuple	54, 28
25	ExprTuple	55, 28
26	Lambda	parameter: 53 body: 29
27	Operation	operator: 30 operand: 33
28	Literal
29	Conditional	value: 32 condition: 38
30	Literal
31	ExprTuple	33
32	Operation	operator: 40 operands: 34
33	Lambda	parameter: 53 body: 35
34	ExprTuple	36, 46
35	Conditional	value: 37 condition: 38
36	Operation	operator: 40 operands: 39
37	Operation	operator: 40 operands: 41
38	Operation	operator: 42 operands: 43
39	ExprTuple	44, 45
40	Literal
41	ExprTuple	45, 46
42	Literal
43	ExprTuple	53, 47
44	Variable
45	Operation	operator: 48 operand: 53
46	Operation	operator: 49 operand: 53
47	Operation	operator: 51 operands: 52
48	Variable
49	Variable
50	ExprTuple	53
51	Literal
52	ExprTuple	54, 55
53	Variable
54	Variable
55	Variable