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 ExprRange, IndexedVar, K, Lambda, V, Variable, a, i, v
from proveit.core_expr_types import a_1_to_i
from proveit.linear_algebra import ScalarMult, VecAdd, VecSpaces
from proveit.logic import Equals, Forall
from proveit.numbers import Complex, Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(K, Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [i], instance_expr = Forall(instance_param_or_params = [a_1_to_i, v], instance_expr = Equals(VecAdd(ExprRange(sub_expr1, ScalarMult(IndexedVar(a, sub_expr1), v), one, i)), ScalarMult(VecAdd(a_1_to_i), v)).with_wrapping_at(2), domains = [Complex, V]), domain = Natural), domain = 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())

K \mapsto \left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{i \in \mathbb{N}}~\left[\forall_{\left(a_{1} \in \mathbb{C}\right), \left(a_{2} \in \mathbb{C}\right), \ldots, \left(a_{i} \in \mathbb{C}\right), v \in V}~\left(\begin{array}{c} \begin{array}{l} \left(\left(a_{1} \cdot v\right) +  \left(a_{2} \cdot v\right) +  \ldots +  \left(a_{i} \cdot v\right)\right) =  \\ \left(\left(a_{1} +  a_{2} +  \ldots +  a_{i}\right) \cdot v\right) \end{array} \end{array}\right)\right]\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: 19 body: 1
1	Operation	operator: 20 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 44 body: 5
4	ExprTuple	44
5	Conditional	value: 6 condition: 7
6	Operation	operator: 20 operand: 11
7	Operation	operator: 9 operands: 10
8	ExprTuple	11
9	Literal
10	ExprTuple	44, 12
11	Lambda	parameter: 57 body: 14
12	Operation	operator: 15 operand: 19
13	ExprTuple	57
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 20 operand: 23
18	Operation	operator: 48 operands: 22
19	Variable
20	Literal
21	ExprTuple	23
22	ExprTuple	57, 24
23	Lambda	parameters: 25 body: 26
24	Literal
25	ExprTuple	51, 58
26	Conditional	value: 27 condition: 28
27	Operation	operator: 29 operands: 30
28	Operation	operator: 31 operands: 32
29	Literal
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35, 36
33	Operation	operator: 46 operands: 37
34	Operation	operator: 53 operands: 38
35	ExprRange	lambda_map: 39 start_index: 56 end_index: 57
36	Operation	operator: 48 operands: 40
37	ExprTuple	41
38	ExprTuple	42, 58
39	Lambda	parameter: 62 body: 43
40	ExprTuple	58, 44
41	ExprRange	lambda_map: 45 start_index: 56 end_index: 57
42	Operation	operator: 46 operands: 47
43	Operation	operator: 48 operands: 49
44	Variable
45	Lambda	parameter: 62 body: 50
46	Literal
47	ExprTuple	51
48	Literal
49	ExprTuple	59, 52
50	Operation	operator: 53 operands: 54
51	ExprRange	lambda_map: 55 start_index: 56 end_index: 57
52	Literal
53	Literal
54	ExprTuple	59, 58
55	Lambda	parameter: 62 body: 59
56	Literal
57	Variable
58	Variable
59	IndexedVar	variable: 60 index: 62
60	Variable
61	ExprTuple	62
62	Variable