Expression of type Conditional

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, 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 = 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(\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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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