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, i, j, k, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Exp, Integer, Interval, LessEq, Sum, frac, one, subtract

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([j, k], Conditional(Equals(Sum(index_or_indices = [i], summand = Exp(x, i), domain = Interval(j, k)), frac(subtract(Exp(x, j), Exp(x, Add(k, one))), subtract(one, x))), And(InSet(j, Integer), InSet(k, Integer), LessEq(j, k)))))

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(j, k\right) \mapsto \left\{\left(\sum_{i = j}^{k} x^{i}\right) = \frac{x^{j} - x^{k + 1}}{1 - x} \textrm{ if } j \in \mathbb{Z} ,  k \in \mathbb{Z} ,  j \leq k\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: 45 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: 14 operand: 21
10	Operation	operator: 16 operands: 17
11	Operation	operator: 35 operands: 18
12	Operation	operator: 35 operands: 19
13	Operation	operator: 20 operands: 45
14	Literal
15	ExprTuple	21
16	Literal
17	ExprTuple	22, 23
18	ExprTuple	48, 24
19	ExprTuple	53, 24
20	Literal
21	Lambda	parameter: 41 body: 26
22	Operation	operator: 51 operands: 27
23	Operation	operator: 51 operands: 28
24	Literal
25	ExprTuple	41
26	Conditional	value: 29 condition: 30
27	ExprTuple	31, 32
28	ExprTuple	54, 33
29	Operation	operator: 46 operands: 34
30	Operation	operator: 35 operands: 36
31	Operation	operator: 46 operands: 37
32	Operation	operator: 39 operand: 43
33	Operation	operator: 39 operand: 49
34	ExprTuple	49, 41
35	Literal
36	ExprTuple	41, 42
37	ExprTuple	49, 48
38	ExprTuple	43
39	Literal
40	ExprTuple	49
41	Variable
42	Operation	operator: 44 operands: 45
43	Operation	operator: 46 operands: 47
44	Literal
45	ExprTuple	48, 53
46	Literal
47	ExprTuple	49, 50
48	Variable
49	Variable
50	Operation	operator: 51 operands: 52
51	Literal
52	ExprTuple	53, 54
53	Variable
54	Literal