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

# build up the expression from sub-expressions
expr = Lambda(V, Conditional(Forall(instance_param_or_params = [k], instance_expr = Implies(InSet(vec_summation_b1toj_fQ, V), Equals(VecSum(index_or_indices = [b_1_to_j], summand = ScalarMult(k, f__b_1_to_j), condition = Q__b_1_to_j), ScalarMult(k, vec_summation_b1toj_fQ)).with_wrapping_at(1)).with_wrapping_at(2), domain = K), 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_{k \in K}~\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 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(k \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)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\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: 27 body: 2
1	ExprTuple	27
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	27, 10
9	Lambda	parameter: 42 body: 12
10	Operation	operator: 13 operand: 22
11	ExprTuple	42
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	22
15	Operation	operator: 17 operands: 18
16	Operation	operator: 23 operands: 19
17	Literal
18	ExprTuple	20, 21
19	ExprTuple	42, 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	Variable
23	Literal
24	ExprTuple	33, 27
25	Literal
26	ExprTuple	28, 29
27	Variable
28	Operation	operator: 35 operand: 32
29	Operation	operator: 39 operands: 31
30	ExprTuple	32
31	ExprTuple	42, 33
32	Lambda	parameters: 47 body: 34
33	Operation	operator: 35 operand: 38
34	Conditional	value: 37 condition: 44
35	Literal
36	ExprTuple	38
37	Operation	operator: 39 operands: 40
38	Lambda	parameters: 47 body: 41
39	Literal
40	ExprTuple	42, 43
41	Conditional	value: 43 condition: 44
42	Variable
43	Operation	operator: 45 operands: 47
44	Operation	operator: 46 operands: 47
45	Variable
46	Variable
47	ExprTuple	48
48	ExprRange	lambda_map: 49 start_index: 50 end_index: 51
49	Lambda	parameter: 55 body: 52
50	Literal
51	Variable
52	IndexedVar	variable: 53 index: 55
53	Variable
54	ExprTuple	55
55	Variable