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, 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), And(LessEq(a, b), LessEq(b, c)).with_total_ordering_style())))

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 \leq 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	55, 60, 57
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 19 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	10, 11, 12, 13
8	Operation	operator: 29 operand: 21
9	Operation	operator: 58 operands: 15
10	Operation	operator: 47 operands: 16
11	Operation	operator: 47 operands: 17
12	Operation	operator: 47 operands: 18
13	Operation	operator: 19 operands: 20
14	ExprTuple	21
15	ExprTuple	22, 23
16	ExprTuple	55, 24
17	ExprTuple	60, 24
18	ExprTuple	57, 24
19	Literal
20	ExprTuple	25, 26
21	Lambda	parameter: 50 body: 27
22	Operation	operator: 29 operand: 34
23	Operation	operator: 29 operand: 35
24	Literal
25	Operation	operator: 31 operands: 52
26	Operation	operator: 31 operands: 32
27	Conditional	value: 41 condition: 33
28	ExprTuple	34
29	Literal
30	ExprTuple	35
31	Literal
32	ExprTuple	60, 57
33	Operation	operator: 47 operands: 36
34	Lambda	parameter: 50 body: 37
35	Lambda	parameter: 50 body: 38
36	ExprTuple	50, 39
37	Conditional	value: 41 condition: 40
38	Conditional	value: 41 condition: 42
39	Operation	operator: 53 operands: 43
40	Operation	operator: 47 operands: 44
41	Operation	operator: 45 operand: 50
42	Operation	operator: 47 operands: 48
43	ExprTuple	55, 57
44	ExprTuple	50, 49
45	Variable
46	ExprTuple	50
47	Literal
48	ExprTuple	50, 51
49	Operation	operator: 53 operands: 52
50	Variable
51	Operation	operator: 53 operands: 54
52	ExprTuple	55, 60
53	Literal
54	ExprTuple	56, 57
55	Variable
56	Operation	operator: 58 operands: 59
57	Variable
58	Literal
59	ExprTuple	60, 61
60	Variable
61	Literal