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, a, b, c, f, fx, x
from proveit.logic import And, Equals, Forall
from proveit.numbers import Add, Integer, Interval, LessEq, Sum, one

# 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, c)), Add(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(Add(b, one), c)))), domain = Integer, condition = And(LessEq(a, b), LessEq(b, c)).with_total_ordering_style())))

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}~|~a \leq b \leq c}~\left(\left(\sum_{x = a}^{c} f\left(x\right)\right) = \left(\left(\sum_{x = a}^{b} f\left(x\right)\right) + \left(\sum_{x = b + 1}^{c} f\left(x\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	parameter: 51 body: 3
2	ExprTuple	51
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 7 body: 8
7	ExprTuple	61, 66, 63
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 25 operands: 13
11	Literal
12	ExprTuple	14, 15
13	ExprTuple	16, 17, 18, 19
14	Operation	operator: 35 operand: 27
15	Operation	operator: 64 operands: 21
16	Operation	operator: 53 operands: 22
17	Operation	operator: 53 operands: 23
18	Operation	operator: 53 operands: 24
19	Operation	operator: 25 operands: 26
20	ExprTuple	27
21	ExprTuple	28, 29
22	ExprTuple	61, 30
23	ExprTuple	66, 30
24	ExprTuple	63, 30
25	Literal
26	ExprTuple	31, 32
27	Lambda	parameter: 56 body: 33
28	Operation	operator: 35 operand: 40
29	Operation	operator: 35 operand: 41
30	Literal
31	Operation	operator: 37 operands: 58
32	Operation	operator: 37 operands: 38
33	Conditional	value: 47 condition: 39
34	ExprTuple	40
35	Literal
36	ExprTuple	41
37	Literal
38	ExprTuple	66, 63
39	Operation	operator: 53 operands: 42
40	Lambda	parameter: 56 body: 43
41	Lambda	parameter: 56 body: 44
42	ExprTuple	56, 45
43	Conditional	value: 47 condition: 46
44	Conditional	value: 47 condition: 48
45	Operation	operator: 59 operands: 49
46	Operation	operator: 53 operands: 50
47	Operation	operator: 51 operand: 56
48	Operation	operator: 53 operands: 54
49	ExprTuple	61, 63
50	ExprTuple	56, 55
51	Variable
52	ExprTuple	56
53	Literal
54	ExprTuple	56, 57
55	Operation	operator: 59 operands: 58
56	Variable
57	Operation	operator: 59 operands: 60
58	ExprTuple	61, 66
59	Literal
60	ExprTuple	62, 63
61	Variable
62	Operation	operator: 64 operands: 65
63	Variable
64	Literal
65	ExprTuple	66, 67
66	Variable
67	Literal