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, a, b, fa, fx, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Integer, Interval, Less, Sum, one

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

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\right) \mapsto \left\{\left(\sum_{x = a}^{b} f\left(x\right)\right) = \left(f\left(a\right) + \left(\sum_{x = a + 1}^{b} f\left(x\right)\right)\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  a < b\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: 34 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 25 operand: 19
10	Operation	operator: 45 operands: 15
11	Operation	operator: 37 operands: 16
12	Operation	operator: 37 operands: 17
13	Operation	operator: 18 operands: 34
14	ExprTuple	19
15	ExprTuple	20, 21
16	ExprTuple	47, 22
17	ExprTuple	44, 22
18	Literal
19	Lambda	parameter: 39 body: 23
20	Operation	operator: 35 operand: 47
21	Operation	operator: 25 operand: 28
22	Literal
23	Conditional	value: 32 condition: 27
24	ExprTuple	47
25	Literal
26	ExprTuple	28
27	Operation	operator: 37 operands: 29
28	Lambda	parameter: 39 body: 30
29	ExprTuple	39, 31
30	Conditional	value: 32 condition: 33
31	Operation	operator: 41 operands: 34
32	Operation	operator: 35 operand: 39
33	Operation	operator: 37 operands: 38
34	ExprTuple	47, 44
35	Variable
36	ExprTuple	39
37	Literal
38	ExprTuple	39, 40
39	Variable
40	Operation	operator: 41 operands: 42
41	Literal
42	ExprTuple	43, 44
43	Operation	operator: 45 operands: 46
44	Variable
45	Literal
46	ExprTuple	47, 48
47	Variable
48	Literal