Expression of type Forall

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 fi, i, j, k, x
from proveit.logic import Equals, Forall
from proveit.numbers import Integer, Interval, Mult, Sum

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(j, k)
expr = Forall(instance_param_or_params = [j, k], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = Mult(x, fi), domain = sub_expr2), Mult(x, Sum(index_or_indices = sub_expr1, summand = fi, domain = sub_expr2))), domain = Integer)

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_{j, k \in \mathbb{Z}}~\left(\left(\sum_{i = j}^{k} \left(x \cdot f\left(i\right)\right)\right) = \left(x \cdot \left(\sum_{i = j}^{k} f\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: 40 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
11	Operation	operator: 23 operand: 19
12	Operation	operator: 27 operands: 16
13	Operation	operator: 35 operands: 17
14	Operation	operator: 35 operands: 18
15	ExprTuple	19
16	ExprTuple	30, 20
17	ExprTuple	41, 21
18	ExprTuple	42, 21
19	Lambda	parameter: 37 body: 22
20	Operation	operator: 23 operand: 26
21	Literal
22	Conditional	value: 25 condition: 32
23	Literal
24	ExprTuple	26
25	Operation	operator: 27 operands: 28
26	Lambda	parameter: 37 body: 29
27	Literal
28	ExprTuple	30, 31
29	Conditional	value: 31 condition: 32
30	Variable
31	Operation	operator: 33 operand: 37
32	Operation	operator: 35 operands: 36
33	Variable
34	ExprTuple	37
35	Literal
36	ExprTuple	37, 38
37	Variable
38	Operation	operator: 39 operands: 40
39	Literal
40	ExprTuple	41, 42
41	Variable
42	Variable