Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 44 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12
8	Operation	operator: 13 operand: 20
9	Operation	operator: 15 operands: 16
10	Operation	operator: 34 operands: 17
11	Operation	operator: 34 operands: 18
12	Operation	operator: 19 operands: 44
13	Literal
14	ExprTuple	20
15	Literal
16	ExprTuple	21, 22
17	ExprTuple	47, 23
18	ExprTuple	52, 23
19	Literal
20	Lambda	parameter: 40 body: 25
21	Operation	operator: 50 operands: 26
22	Operation	operator: 50 operands: 27
23	Literal
24	ExprTuple	40
25	Conditional	value: 28 condition: 29
26	ExprTuple	30, 31
27	ExprTuple	53, 32
28	Operation	operator: 45 operands: 33
29	Operation	operator: 34 operands: 35
30	Operation	operator: 45 operands: 36
31	Operation	operator: 38 operand: 42
32	Operation	operator: 38 operand: 48
33	ExprTuple	48, 40
34	Literal
35	ExprTuple	40, 41
36	ExprTuple	48, 47
37	ExprTuple	42
38	Literal
39	ExprTuple	48
40	Variable
41	Operation	operator: 43 operands: 44
42	Operation	operator: 45 operands: 46
43	Literal
44	ExprTuple	47, 52
45	Literal
46	ExprTuple	48, 49
47	Variable
48	Variable
49	Operation	operator: 50 operands: 51
50	Literal
51	ExprTuple	52, 53
52	Variable
53	Literal