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 ExprRange, IndexedVar, Variable, a, c, l
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Complex, Integer, Mult, Sum, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [l]
sub_expr3 = IndexedVar(a, one)
sub_expr4 = Add(l, one)
sub_expr5 = ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, zero)
expr = Forall(instance_param_or_params = [sub_expr3, sub_expr5], instance_expr = Equals(Mult(sub_expr3, Sum(index_or_indices = sub_expr2, summand = sub_expr4, domain = Integer), sub_expr5), Sum(index_or_indices = sub_expr2, summand = Mult(sub_expr3, sub_expr4, sub_expr5), domain = Integer)).with_wrapping_at(2), domain = Complex).with_wrapping()

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())

\begin{array}{l}\forall_{a_{1}, c_{1}, c_{2}, \ldots, c_{0} \in \mathbb{C}}~\\
\left(\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot \left[\sum_{l \in \mathbb{Z}}~\left(l + 1\right)\right]\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{0}\right) =  \\ \left[\sum_{l \in \mathbb{Z}}~\left(a_{1} \cdot \left(l + 1\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{0}\right)\right] \end{array} \end{array}\right)\end{array}

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	True	('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	35, 37
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
12	Operation	operator: 32 operands: 16
13	Operation	operator: 23 operand: 21
14	Operation	operator: 38 operands: 18
15	ExprRange	lambda_map: 19 start_index: 48 end_index: 45
16	ExprTuple	35, 20, 37
17	ExprTuple	21
18	ExprTuple	35, 29
19	Lambda	parameter: 52 body: 22
20	Operation	operator: 23 operand: 27
21	Lambda	parameter: 47 body: 25
22	Operation	operator: 38 operands: 26
23	Literal
24	ExprTuple	27
25	Conditional	value: 28 condition: 34
26	ExprTuple	49, 29
27	Lambda	parameter: 47 body: 31
28	Operation	operator: 32 operands: 33
29	Literal
30	ExprTuple	47
31	Conditional	value: 36 condition: 34
32	Literal
33	ExprTuple	35, 36, 37
34	Operation	operator: 38 operands: 39
35	IndexedVar	variable: 40 index: 48
36	Operation	operator: 42 operands: 43
37	ExprRange	lambda_map: 44 start_index: 48 end_index: 45
38	Literal
39	ExprTuple	47, 46
40	Variable
41	ExprTuple	48
42	Literal
43	ExprTuple	47, 48
44	Lambda	parameter: 52 body: 49
45	Literal
46	Literal
47	Variable
48	Literal
49	IndexedVar	variable: 50 index: 52
50	Variable
51	ExprTuple	52
52	Variable