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, a, b, c, f, fx, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Integer, Interval, Sum, subtract

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda([a, b, c], Conditional(Equals(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = Function(f, [subtract(x, c)]), domain = Interval(Add(a, c), Add(b, c)))), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer)))))

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(a, b, c\right) \mapsto \left\{\left(\sum_{x = a}^{b} f\left(x\right)\right) = \left(\sum_{x = a + c}^{b + c} f\left(x - c\right)\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z}\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	52, 53, 54
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: 16 operand: 21
11	Operation	operator: 16 operand: 22
12	Operation	operator: 34 operands: 18
13	Operation	operator: 34 operands: 19
14	Operation	operator: 34 operands: 20
15	ExprTuple	21
16	Literal
17	ExprTuple	22
18	ExprTuple	52, 23
19	ExprTuple	53, 23
20	ExprTuple	54, 23
21	Lambda	parameter: 43 body: 24
22	Lambda	parameter: 43 body: 25
23	Literal
24	Conditional	value: 26 condition: 27
25	Conditional	value: 28 condition: 29
26	Operation	operator: 32 operand: 43
27	Operation	operator: 34 operands: 31
28	Operation	operator: 32 operand: 37
29	Operation	operator: 34 operands: 35
30	ExprTuple	43
31	ExprTuple	43, 36
32	Variable
33	ExprTuple	37
34	Literal
35	ExprTuple	43, 38
36	Operation	operator: 41 operands: 39
37	Operation	operator: 50 operands: 40
38	Operation	operator: 41 operands: 42
39	ExprTuple	52, 53
40	ExprTuple	43, 44
41	Literal
42	ExprTuple	45, 46
43	Variable
44	Operation	operator: 47 operand: 54
45	Operation	operator: 50 operands: 49
46	Operation	operator: 50 operands: 51
47	Literal
48	ExprTuple	54
49	ExprTuple	52, 54
50	Literal
51	ExprTuple	53, 54
52	Variable
53	Variable
54	Variable