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

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Lambda([a, b], Conditional(Equals(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, b)), Add(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, subtract(b, one))), fb)), 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(a, b\right) \mapsto \left\{\left(\sum_{x = a}^{b} f\left(x\right)\right) = \left(\left(\sum_{x = a}^{b - 1} f\left(x\right)\right) + f\left(b\right)\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  a < b\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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