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 Lambda, a, b, c, f, fx, x
from proveit.logic import And, Equals, Forall
from proveit.numbers import Add, Integer, Interval, LessEq, Sum, one

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Lambda(f, Forall(instance_param_or_params = [a, b, c], instance_expr = 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)))), domain = Integer, condition = 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())

f \mapsto \left[\forall_{a, b, c \in \mathbb{Z}~|~a \leq b \leq c}~\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)\right)\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 50 body: 2
1	ExprTuple	50
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameters: 6 body: 7
6	ExprTuple	60, 65, 62
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 24 operands: 12
10	Literal
11	ExprTuple	13, 14
12	ExprTuple	15, 16, 17, 18
13	Operation	operator: 34 operand: 26
14	Operation	operator: 63 operands: 20
15	Operation	operator: 52 operands: 21
16	Operation	operator: 52 operands: 22
17	Operation	operator: 52 operands: 23
18	Operation	operator: 24 operands: 25
19	ExprTuple	26
20	ExprTuple	27, 28
21	ExprTuple	60, 29
22	ExprTuple	65, 29
23	ExprTuple	62, 29
24	Literal
25	ExprTuple	30, 31
26	Lambda	parameter: 55 body: 32
27	Operation	operator: 34 operand: 39
28	Operation	operator: 34 operand: 40
29	Literal
30	Operation	operator: 36 operands: 57
31	Operation	operator: 36 operands: 37
32	Conditional	value: 46 condition: 38
33	ExprTuple	39
34	Literal
35	ExprTuple	40
36	Literal
37	ExprTuple	65, 62
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	Operation	operator: 50 operand: 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