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, Function, Lambda, a, b, c, f, fx, x
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Integer, Interval, Sum, subtract

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda(f, Forall(instance_param_or_params = [a, b, c], instance_expr = 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)))), domain = 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(f \mapsto \left[\forall_{a, b, c \in \mathbb{Z}}~\left(\left(\sum_{x = a}^{b} f\left(x\right)\right) = \left(\sum_{x = a + c}^{b + c} f\left(x - c\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	parameter: 37 body: 3
2	ExprTuple	37
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 7 body: 8
7	ExprTuple	57, 58, 59
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18, 19
15	Operation	operator: 21 operand: 26
16	Operation	operator: 21 operand: 27
17	Operation	operator: 39 operands: 23
18	Operation	operator: 39 operands: 24
19	Operation	operator: 39 operands: 25
20	ExprTuple	26
21	Literal
22	ExprTuple	27
23	ExprTuple	57, 28
24	ExprTuple	58, 28
25	ExprTuple	59, 28
26	Lambda	parameter: 48 body: 29
27	Lambda	parameter: 48 body: 30
28	Literal
29	Conditional	value: 31 condition: 32
30	Conditional	value: 33 condition: 34
31	Operation	operator: 37 operand: 48
32	Operation	operator: 39 operands: 36
33	Operation	operator: 37 operand: 42
34	Operation	operator: 39 operands: 40
35	ExprTuple	48
36	ExprTuple	48, 41
37	Variable
38	ExprTuple	42
39	Literal
40	ExprTuple	48, 43
41	Operation	operator: 46 operands: 44
42	Operation	operator: 55 operands: 45
43	Operation	operator: 46 operands: 47
44	ExprTuple	57, 58
45	ExprTuple	48, 49
46	Literal
47	ExprTuple	50, 51
48	Variable
49	Operation	operator: 52 operand: 59
50	Operation	operator: 55 operands: 54
51	Operation	operator: 55 operands: 56
52	Literal
53	ExprTuple	59
54	ExprTuple	57, 59
55	Literal
56	ExprTuple	58, 59
57	Variable
58	Variable
59	Variable