Expression of type Conditional

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 Conditional, Q, f, j
from proveit.core_expr_types import Q__b_1_to_j, b_1_to_j, f__b_1_to_j
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import Complex, NaturalPos
from proveit.numbers.summation import summation_b1toj_fQ

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [f, Q], instance_expr = Implies(Forall(instance_param_or_params = [b_1_to_j], instance_expr = InSet(f__b_1_to_j, Complex), condition = Q__b_1_to_j), Equals(vec_summation_b1toj_fQ, summation_b1toj_fQ)).with_wrapping_at(2)), InSet(j, NaturalPos))

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())

\left\{\forall_{f, Q}~\left(\begin{array}{c} \begin{array}{l} \left[\forall_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(f\left(b_{1}, b_{2}, \ldots, b_{j}\right) \in \mathbb{C}\right)\right] \Rightarrow  \\ \left(\left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right] = \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right]\right) \end{array} \end{array}\right) \textrm{ if } j \in \mathbb{N}^+\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 13 operand: 5
2	Operation	operator: 26 operands: 4
3	ExprTuple	5
4	ExprTuple	38, 6
5	Lambda	parameters: 7 body: 8
6	Literal
7	ExprTuple	32, 33
8	Operation	operator: 9 operands: 10
9	Literal
10	ExprTuple	11, 12
11	Operation	operator: 13 operand: 17
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17
15	Literal
16	ExprTuple	18, 19
17	Lambda	parameters: 34 body: 20
18	Operation	operator: 21 operand: 25
19	Operation	operator: 22 operand: 25
20	Conditional	value: 24 condition: 31
21	Literal
22	Literal
23	ExprTuple	25
24	Operation	operator: 26 operands: 27
25	Lambda	parameters: 34 body: 28
26	Literal
27	ExprTuple	30, 29
28	Conditional	value: 30 condition: 31
29	Literal
30	Operation	operator: 32 operands: 34
31	Operation	operator: 33 operands: 34
32	Variable
33	Variable
34	ExprTuple	35
35	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
36	Lambda	parameter: 42 body: 39
37	Literal
38	Variable
39	IndexedVar	variable: 40 index: 42
40	Variable
41	ExprTuple	42
42	Variable