Expression of type Lambda

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, Lambda, 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 = Lambda(j, 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())

j \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 40 body: 2
1	ExprTuple	40
2	Conditional	value: 3 condition: 4
3	Operation	operator: 15 operand: 7
4	Operation	operator: 28 operands: 6
5	ExprTuple	7
6	ExprTuple	40, 8
7	Lambda	parameters: 9 body: 10
8	Literal
9	ExprTuple	34, 35
10	Operation	operator: 11 operands: 12
11	Literal
12	ExprTuple	13, 14
13	Operation	operator: 15 operand: 19
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19
17	Literal
18	ExprTuple	20, 21
19	Lambda	parameters: 36 body: 22
20	Operation	operator: 23 operand: 27
21	Operation	operator: 24 operand: 27
22	Conditional	value: 26 condition: 33
23	Literal
24	Literal
25	ExprTuple	27
26	Operation	operator: 28 operands: 29
27	Lambda	parameters: 36 body: 30
28	Literal
29	ExprTuple	32, 31
30	Conditional	value: 32 condition: 33
31	Literal
32	Operation	operator: 34 operands: 36
33	Operation	operator: 35 operands: 36
34	Variable
35	Variable
36	ExprTuple	37
37	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
38	Lambda	parameter: 44 body: 41
39	Literal
40	Variable
41	IndexedVar	variable: 42 index: 44
42	Variable
43	ExprTuple	44
44	Variable