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, K, Lambda, V, v
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.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import Equals, Implies, InSet
from proveit.numbers import Sum

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
expr = Lambda(v, Conditional(Implies(InSet(vec_summation_b1toj_fQ, K), Equals(ScalarMult(Sum(index_or_indices = sub_expr1, summand = f__b_1_to_j, condition = Q__b_1_to_j), v), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(f__b_1_to_j, v), condition = Q__b_1_to_j)).with_wrapping_at(1)).with_wrapping_at(2), InSet(v, V)))

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())

v \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)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right] \in K\right) \Rightarrow  \\ \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)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right] \cdot v\right) \\  = \left[\sum_{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) \cdot v\right)\right] \end{array} \end{array}\right) \end{array} \end{array} \textrm{ if } v \in V\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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