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 V, i, j, k, v
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Interval, one, subtract

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [v], instance_expr = Equals(VecSum(index_or_indices = [i], summand = v, domain = Interval(j, k)), ScalarMult(Add(subtract(k, j), one), v)), domain = V)

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_{v \in V}~\left(\left(\sum_{i=j}^{k} v\right) = \left(\left(\left(k - j\right) + 1\right) \cdot v\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	parameter: 23 body: 5
4	ExprTuple	23
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 27 operands: 10
8	Literal
9	ExprTuple	11, 12
10	ExprTuple	23, 13
11	Operation	operator: 14 operand: 18
12	Operation	operator: 16 operands: 17
13	Variable
14	Literal
15	ExprTuple	18
16	Literal
17	ExprTuple	19, 23
18	Lambda	parameter: 31 body: 21
19	Operation	operator: 29 operands: 22
20	ExprTuple	31
21	Conditional	value: 23 condition: 24
22	ExprTuple	25, 26
23	Variable
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	Literal
27	Literal
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	38, 33
31	Variable
32	Operation	operator: 34 operands: 35
33	Operation	operator: 36 operand: 39
34	Literal
35	ExprTuple	39, 38
36	Literal
37	ExprTuple	39
38	Variable
39	Variable