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, c, fx, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Integer, Interval, Less, LessEq, Sum, one

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

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, c\right) \mapsto \left\{\left(\sum_{x = a}^{c} f\left(x\right)\right) = \left(\left(\sum_{x = a}^{b} f\left(x\right)\right) + \left(\sum_{x = b + 1}^{c} f\left(x\right)\right)\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  a \leq b ,  b < c\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	54, 59, 56
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, 14, 15
9	Operation	operator: 30 operand: 24
10	Operation	operator: 57 operands: 17
11	Operation	operator: 46 operands: 18
12	Operation	operator: 46 operands: 19
13	Operation	operator: 46 operands: 20
14	Operation	operator: 21 operands: 51
15	Operation	operator: 22 operands: 23
16	ExprTuple	24
17	ExprTuple	25, 26
18	ExprTuple	54, 27
19	ExprTuple	59, 27
20	ExprTuple	56, 27
21	Literal
22	Literal
23	ExprTuple	59, 56
24	Lambda	parameter: 49 body: 28
25	Operation	operator: 30 operand: 33
26	Operation	operator: 30 operand: 34
27	Literal
28	Conditional	value: 40 condition: 32
29	ExprTuple	33
30	Literal
31	ExprTuple	34
32	Operation	operator: 46 operands: 35
33	Lambda	parameter: 49 body: 36
34	Lambda	parameter: 49 body: 37
35	ExprTuple	49, 38
36	Conditional	value: 40 condition: 39
37	Conditional	value: 40 condition: 41
38	Operation	operator: 52 operands: 42
39	Operation	operator: 46 operands: 43
40	Operation	operator: 44 operand: 49
41	Operation	operator: 46 operands: 47
42	ExprTuple	54, 56
43	ExprTuple	49, 48
44	Variable
45	ExprTuple	49
46	Literal
47	ExprTuple	49, 50
48	Operation	operator: 52 operands: 51
49	Variable
50	Operation	operator: 52 operands: 53
51	ExprTuple	54, 59
52	Literal
53	ExprTuple	55, 56
54	Variable
55	Operation	operator: 57 operands: 58
56	Variable
57	Literal
58	ExprTuple	59, 60
59	Variable
60	Literal