Expression of type Forall

from the theory of proveit.linear_algebra.addition

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 a, b, c, i, vi
from proveit.linear_algebra import VecAdd, VecSum
from proveit.logic import Equals, Forall
from proveit.numbers import Integer, Interval, Less, LessEq, one, subtract

# build up the expression from sub-expressions
sub_expr1 = [i]
expr = Forall(instance_param_or_params = [a, b, c], instance_expr = Equals(VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(a, c)), VecAdd(VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(a, subtract(b, one))), VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(b, c)))), domain = Integer, conditions = [Less(a, b), LessEq(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())

\forall_{a, b, c \in \mathbb{Z}~|~a < b, b \leq c}~\left(\left(\sum_{i=a}^{c} v\left(i\right)\right) = \left(\left(\sum_{i=a}^{b - 1} v\left(i\right)\right) + \left(\sum_{i=b}^{c} v\left(i\right)\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	58, 63, 60
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15, 16, 17, 18
12	Operation	operator: 34 operand: 28
13	Operation	operator: 20 operands: 21
14	Operation	operator: 50 operands: 22
15	Operation	operator: 50 operands: 23
16	Operation	operator: 50 operands: 24
17	Operation	operator: 25 operands: 26
18	Operation	operator: 27 operands: 57
19	ExprTuple	28
20	Literal
21	ExprTuple	29, 30
22	ExprTuple	58, 31
23	ExprTuple	63, 31
24	ExprTuple	60, 31
25	Literal
26	ExprTuple	58, 63
27	Literal
28	Lambda	parameter: 53 body: 32
29	Operation	operator: 34 operand: 37
30	Operation	operator: 34 operand: 38
31	Literal
32	Conditional	value: 44 condition: 36
33	ExprTuple	37
34	Literal
35	ExprTuple	38
36	Operation	operator: 50 operands: 39
37	Lambda	parameter: 53 body: 40
38	Lambda	parameter: 53 body: 41
39	ExprTuple	53, 42
40	Conditional	value: 44 condition: 43
41	Conditional	value: 44 condition: 45
42	Operation	operator: 56 operands: 46
43	Operation	operator: 50 operands: 47
44	Operation	operator: 48 operand: 53
45	Operation	operator: 50 operands: 51
46	ExprTuple	58, 60
47	ExprTuple	53, 52
48	Variable
49	ExprTuple	53
50	Literal
51	ExprTuple	53, 54
52	Operation	operator: 56 operands: 55
53	Variable
54	Operation	operator: 56 operands: 57
55	ExprTuple	58, 59
56	Literal
57	ExprTuple	63, 60
58	Variable
59	Operation	operator: 61 operands: 62
60	Variable
61	Literal
62	ExprTuple	63, 64
63	Variable
64	Operation	operator: 65 operand: 67
65	Literal
66	ExprTuple	67
67	Literal