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 Complex, 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 = [x], instance_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), domain = Complex)

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_{x \in \mathbb{C}}~\left[\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)\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 38 body: 4
3	ExprTuple	38
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 43 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	38, 11
10	Lambda	parameters: 48 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 31 operand: 27
20	Operation	operator: 35 operands: 24
21	Operation	operator: 43 operands: 25
22	Operation	operator: 43 operands: 26
23	ExprTuple	27
24	ExprTuple	38, 28
25	ExprTuple	49, 29
26	ExprTuple	50, 29
27	Lambda	parameter: 45 body: 30
28	Operation	operator: 31 operand: 34
29	Literal
30	Conditional	value: 33 condition: 40
31	Literal
32	ExprTuple	34
33	Operation	operator: 35 operands: 36
34	Lambda	parameter: 45 body: 37
35	Literal
36	ExprTuple	38, 39
37	Conditional	value: 39 condition: 40
38	Variable
39	Operation	operator: 41 operand: 45
40	Operation	operator: 43 operands: 44
41	Variable
42	ExprTuple	45
43	Literal
44	ExprTuple	45, 46
45	Variable
46	Operation	operator: 47 operands: 48
47	Literal
48	ExprTuple	49, 50
49	Variable
50	Variable