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 Equals, Forall
from proveit.numbers import Add, Integer, Interval, Less, 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, conditions = [LessEq(a, b), Less(b, c)])))

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, b < 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: 50 body: 3
2	ExprTuple	50
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 7 body: 8
7	ExprTuple	60, 65, 62
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, 20, 21
15	Operation	operator: 36 operand: 30
16	Operation	operator: 63 operands: 23
17	Operation	operator: 52 operands: 24
18	Operation	operator: 52 operands: 25
19	Operation	operator: 52 operands: 26
20	Operation	operator: 27 operands: 57
21	Operation	operator: 28 operands: 29
22	ExprTuple	30
23	ExprTuple	31, 32
24	ExprTuple	60, 33
25	ExprTuple	65, 33
26	ExprTuple	62, 33
27	Literal
28	Literal
29	ExprTuple	65, 62
30	Lambda	parameter: 55 body: 34
31	Operation	operator: 36 operand: 39
32	Operation	operator: 36 operand: 40
33	Literal
34	Conditional	value: 46 condition: 38
35	ExprTuple	39
36	Literal
37	ExprTuple	40
38	Operation	operator: 52 operands: 41
39	Lambda	parameter: 55 body: 42
40	Lambda	parameter: 55 body: 43
41	ExprTuple	55, 44
42	Conditional	value: 46 condition: 45
43	Conditional	value: 46 condition: 47
44	Operation	operator: 58 operands: 48
45	Operation	operator: 52 operands: 49
46	Operation	operator: 50 operand: 55
47	Operation	operator: 52 operands: 53
48	ExprTuple	60, 62
49	ExprTuple	55, 54
50	Variable
51	ExprTuple	55
52	Literal
53	ExprTuple	55, 56
54	Operation	operator: 58 operands: 57
55	Variable
56	Operation	operator: 58 operands: 59
57	ExprTuple	60, 65
58	Literal
59	ExprTuple	61, 62
60	Variable
61	Operation	operator: 63 operands: 64
62	Variable
63	Literal
64	ExprTuple	65, 66
65	Variable
66	Literal