Expression of type Lambda

from the theory of proveit.linear_algebra.scalar_multiplication

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, Function, K, Lambda, V, c, k
from proveit.core_expr_types import Q__b_1_to_j, b_1_to_j, f__b_1_to_j
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import Equals, Implies, InSet
from proveit.numbers import Mult

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
sub_expr2 = Function(c, sub_expr1)
sub_expr3 = VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, f__b_1_to_j), condition = Q__b_1_to_j)
expr = Lambda(k, Conditional(Implies(InSet(sub_expr3, V), Equals(VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Mult(k, sub_expr2), f__b_1_to_j), condition = Q__b_1_to_j), ScalarMult(k, sub_expr3)).with_wrapping_at(1)).with_wrapping_at(1), InSet(k, K)))

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())

k \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(\left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(c\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right)\right] \in V\right) \\  \Rightarrow \left(\begin{array}{c} \begin{array}{l} \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(\left(k \cdot c\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right)\right] \\  = \left(k \cdot \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(c\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right)\right]\right) \end{array} \end{array}\right) \end{array} \end{array} \textrm{ if } k \in K\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 37 body: 2
1	ExprTuple	37
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 11 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	37, 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	Variable
11	Literal
12	ExprTuple	21, 15
13	Literal
14	ExprTuple	16, 17
15	Variable
16	Operation	operator: 23 operand: 20
17	Operation	operator: 34 operands: 19
18	ExprTuple	20
19	ExprTuple	37, 21
20	Lambda	parameters: 42 body: 22
21	Operation	operator: 23 operand: 26
22	Conditional	value: 25 condition: 31
23	Literal
24	ExprTuple	26
25	Operation	operator: 34 operands: 27
26	Lambda	parameters: 42 body: 28
27	ExprTuple	29, 39
28	Conditional	value: 30 condition: 31
29	Operation	operator: 32 operands: 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 36 operands: 42
32	Literal
33	ExprTuple	37, 38
34	Literal
35	ExprTuple	38, 39
36	Variable
37	Variable
38	Operation	operator: 40 operands: 42
39	Operation	operator: 41 operands: 42
40	Variable
41	Variable
42	ExprTuple	43
43	ExprRange	lambda_map: 44 start_index: 45 end_index: 46
44	Lambda	parameter: 50 body: 47
45	Literal
46	Variable
47	IndexedVar	variable: 48 index: 50
48	Variable
49	ExprTuple	50
50	Variable