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, VecSpaces, VecSum
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import Equals, Forall, Implies, InClass, InSet
from proveit.numbers import Sum

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
expr = Lambda(V, Conditional(Forall(instance_param_or_params = [v], instance_expr = 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), domain = V), InClass(V, VecSpaces(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())

V \mapsto \left\{\forall_{v \in V}~\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}\right) \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 22 body: 2
1	ExprTuple	22
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	22, 10
9	Lambda	parameter: 46 body: 12
10	Operation	operator: 13 operand: 28
11	ExprTuple	46
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	28
15	Operation	operator: 17 operands: 18
16	Operation	operator: 23 operands: 19
17	Literal
18	ExprTuple	20, 21
19	ExprTuple	46, 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	Variable
23	Literal
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	29, 30
27	Operation	operator: 32 operand: 39
28	Variable
29	Operation	operator: 42 operands: 31
30	Operation	operator: 32 operand: 35
31	ExprTuple	34, 46
32	Literal
33	ExprTuple	35
34	Operation	operator: 36 operand: 39
35	Lambda	parameters: 49 body: 38
36	Literal
37	ExprTuple	39
38	Conditional	value: 40 condition: 44
39	Lambda	parameters: 49 body: 41
40	Operation	operator: 42 operands: 43
41	Conditional	value: 45 condition: 44
42	Literal
43	ExprTuple	45, 46
44	Operation	operator: 47 operands: 49
45	Operation	operator: 48 operands: 49
46	Variable
47	Variable
48	Variable
49	ExprTuple	50
50	ExprRange	lambda_map: 51 start_index: 52 end_index: 53
51	Lambda	parameter: 57 body: 54
52	Literal
53	Variable
54	IndexedVar	variable: 55 index: 57
55	Variable
56	ExprTuple	57
57	Variable