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 Equals, Forall
from proveit.numbers import Add, Integer, Interval, Less, 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, conditions = [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())

f \mapsto \left[\forall_{a, b, c \in \mathbb{Z}~|~a \leq b, b < 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: 49 body: 2
1	ExprTuple	49
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameters: 6 body: 7
6	ExprTuple	59, 64, 61
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17, 18, 19, 20
14	Operation	operator: 35 operand: 29
15	Operation	operator: 62 operands: 22
16	Operation	operator: 51 operands: 23
17	Operation	operator: 51 operands: 24
18	Operation	operator: 51 operands: 25
19	Operation	operator: 26 operands: 56
20	Operation	operator: 27 operands: 28
21	ExprTuple	29
22	ExprTuple	30, 31
23	ExprTuple	59, 32
24	ExprTuple	64, 32
25	ExprTuple	61, 32
26	Literal
27	Literal
28	ExprTuple	64, 61
29	Lambda	parameter: 54 body: 33
30	Operation	operator: 35 operand: 38
31	Operation	operator: 35 operand: 39
32	Literal
33	Conditional	value: 45 condition: 37
34	ExprTuple	38
35	Literal
36	ExprTuple	39
37	Operation	operator: 51 operands: 40
38	Lambda	parameter: 54 body: 41
39	Lambda	parameter: 54 body: 42
40	ExprTuple	54, 43
41	Conditional	value: 45 condition: 44
42	Conditional	value: 45 condition: 46
43	Operation	operator: 57 operands: 47
44	Operation	operator: 51 operands: 48
45	Operation	operator: 49 operand: 54
46	Operation	operator: 51 operands: 52
47	ExprTuple	59, 61
48	ExprTuple	54, 53
49	Variable
50	ExprTuple	54
51	Literal
52	ExprTuple	54, 55
53	Operation	operator: 57 operands: 56
54	Variable
55	Operation	operator: 57 operands: 58
56	ExprTuple	59, 64
57	Literal
58	ExprTuple	60, 61
59	Variable
60	Operation	operator: 62 operands: 63
61	Variable
62	Literal
63	ExprTuple	64, 65
64	Variable
65	Literal