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, 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, InClass
from proveit.numbers import Complex, Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(V, Conditional(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), 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_{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] \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: 41 body: 2
1	ExprTuple	41
2	Conditional	value: 3 condition: 4
3	Operation	operator: 17 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	41, 9
8	Lambda	parameter: 54 body: 11
9	Operation	operator: 12 operand: 16
10	ExprTuple	54
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	16
14	Operation	operator: 17 operand: 20
15	Operation	operator: 45 operands: 19
16	Variable
17	Literal
18	ExprTuple	20
19	ExprTuple	54, 21
20	Lambda	parameters: 22 body: 23
21	Literal
22	ExprTuple	48, 55
23	Conditional	value: 24 condition: 25
24	Operation	operator: 26 operands: 27
25	Operation	operator: 28 operands: 29
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32, 33
30	Operation	operator: 43 operands: 34
31	Operation	operator: 50 operands: 35
32	ExprRange	lambda_map: 36 start_index: 53 end_index: 54
33	Operation	operator: 45 operands: 37
34	ExprTuple	38
35	ExprTuple	39, 55
36	Lambda	parameter: 59 body: 40
37	ExprTuple	55, 41
38	ExprRange	lambda_map: 42 start_index: 53 end_index: 54
39	Operation	operator: 43 operands: 44
40	Operation	operator: 45 operands: 46
41	Variable
42	Lambda	parameter: 59 body: 47
43	Literal
44	ExprTuple	48
45	Literal
46	ExprTuple	56, 49
47	Operation	operator: 50 operands: 51
48	ExprRange	lambda_map: 52 start_index: 53 end_index: 54
49	Literal
50	Literal
51	ExprTuple	56, 55
52	Lambda	parameter: 59 body: 56
53	Literal
54	Variable
55	Variable
56	IndexedVar	variable: 57 index: 59
57	Variable
58	ExprTuple	59
59	Variable