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, alpha, b, c, k
from proveit.core_expr_types import alpha_k
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Integer, Interval, LessEq, Sum, one

# build up the expression from sub-expressions
sub_expr1 = [k]
expr = Lambda([a, b, c], Conditional(Forall(instance_param_or_params = [alpha], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(a, c)), Add(Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = alpha_k, 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\{\forall_{\alpha}~\left(\left(\sum_{k = a}^{c} \alpha_{k}\right) = \left(\left(\sum_{k = a}^{b} \alpha_{k}\right) + \left(\sum_{k = b + 1}^{c} \alpha_{k}\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	60, 65, 62
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 18 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10, 11, 12
8	Lambda	parameter: 50 body: 14
9	Operation	operator: 52 operands: 15
10	Operation	operator: 52 operands: 16
11	Operation	operator: 52 operands: 17
12	Operation	operator: 18 operands: 19
13	ExprTuple	50
14	Operation	operator: 20 operands: 21
15	ExprTuple	60, 22
16	ExprTuple	65, 22
17	ExprTuple	62, 22
18	Literal
19	ExprTuple	23, 24
20	Literal
21	ExprTuple	25, 26
22	Literal
23	Operation	operator: 27 operands: 57
24	Operation	operator: 27 operands: 28
25	Operation	operator: 36 operand: 31
26	Operation	operator: 63 operands: 30
27	Literal
28	ExprTuple	65, 62
29	ExprTuple	31
30	ExprTuple	32, 33
31	Lambda	parameter: 55 body: 34
32	Operation	operator: 36 operand: 39
33	Operation	operator: 36 operand: 40
34	Conditional	value: 46 condition: 38
35	ExprTuple	39
36	Literal
37	ExprTuple	40
38	Operation	operator: 52 operands: 41
39	Lambda	parameter: 55 body: 42
40	Lambda	parameter: 55 body: 43
41	ExprTuple	55, 44
42	Conditional	value: 46 condition: 45
43	Conditional	value: 46 condition: 47
44	Operation	operator: 58 operands: 48
45	Operation	operator: 52 operands: 49
46	IndexedVar	variable: 50 index: 55
47	Operation	operator: 52 operands: 53
48	ExprTuple	60, 62
49	ExprTuple	55, 54
50	Variable
51	ExprTuple	55
52	Literal
53	ExprTuple	55, 56
54	Operation	operator: 58 operands: 57
55	Variable
56	Operation	operator: 58 operands: 59
57	ExprTuple	60, 65
58	Literal
59	ExprTuple	61, 62
60	Variable
61	Operation	operator: 63 operands: 64
62	Variable
63	Literal
64	ExprTuple	65, 66
65	Variable
66	Literal