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, i, va, vi
from proveit.linear_algebra import VecAdd, VecSum
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Integer, Interval, Less, one

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

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 \in \mathbb{Z}~|~a < b}~\left(\left(\sum_{i=a}^{b} v\left(i\right)\right) = \left(v\left(a\right) + \left(\sum_{i=a + 1}^{b} 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: 37 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14, 15
11	Operation	operator: 28 operand: 22
12	Operation	operator: 17 operands: 18
13	Operation	operator: 40 operands: 19
14	Operation	operator: 40 operands: 20
15	Operation	operator: 21 operands: 37
16	ExprTuple	22
17	Literal
18	ExprTuple	23, 24
19	ExprTuple	50, 25
20	ExprTuple	47, 25
21	Literal
22	Lambda	parameter: 42 body: 26
23	Operation	operator: 38 operand: 50
24	Operation	operator: 28 operand: 31
25	Literal
26	Conditional	value: 35 condition: 30
27	ExprTuple	50
28	Literal
29	ExprTuple	31
30	Operation	operator: 40 operands: 32
31	Lambda	parameter: 42 body: 33
32	ExprTuple	42, 34
33	Conditional	value: 35 condition: 36
34	Operation	operator: 44 operands: 37
35	Operation	operator: 38 operand: 42
36	Operation	operator: 40 operands: 41
37	ExprTuple	50, 47
38	Variable
39	ExprTuple	42
40	Literal
41	ExprTuple	42, 43
42	Variable
43	Operation	operator: 44 operands: 45
44	Literal
45	ExprTuple	46, 47
46	Operation	operator: 48 operands: 49
47	Variable
48	Literal
49	ExprTuple	50, 51
50	Variable
51	Literal