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, k
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 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 = [k, a_1_to_i], instance_expr = Equals(VecAdd(ExprRange(sub_expr1, ScalarMult(k, IndexedVar(a, sub_expr1)), one, i)), ScalarMult(k, VecAdd(a_1_to_i))).with_wrapping_at(2), domains = [K, 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_{k \in K,\left(a_{1} \in V\right), \left(a_{2} \in V\right), \ldots, \left(a_{i} \in V\right)}~\left(\begin{array}{c} \begin{array}{l} \left(\left(k \cdot a_{1}\right) +  \left(k \cdot a_{2}\right) +  \ldots +  \left(k \cdot a_{i}\right)\right) =  \\ \left(k \cdot \left(a_{1} +  a_{2} +  \ldots +  a_{i}\right)\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: 48 body: 2
1	ExprTuple	48
2	Conditional	value: 3 condition: 4
3	Operation	operator: 16 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	48, 9
8	Lambda	parameter: 53 body: 11
9	Operation	operator: 12 operand: 39
10	ExprTuple	53
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	39
14	Operation	operator: 16 operand: 19
15	Operation	operator: 44 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	53, 20
19	Lambda	parameters: 21 body: 22
20	Literal
21	ExprTuple	54, 47
22	Conditional	value: 23 condition: 24
23	Operation	operator: 25 operands: 26
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	31, 32
29	Operation	operator: 42 operands: 33
30	Operation	operator: 49 operands: 34
31	Operation	operator: 44 operands: 35
32	ExprRange	lambda_map: 36 start_index: 52 end_index: 53
33	ExprTuple	37
34	ExprTuple	54, 38
35	ExprTuple	54, 39
36	Lambda	parameter: 58 body: 40
37	ExprRange	lambda_map: 41 start_index: 52 end_index: 53
38	Operation	operator: 42 operands: 43
39	Variable
40	Operation	operator: 44 operands: 45
41	Lambda	parameter: 58 body: 46
42	Literal
43	ExprTuple	47
44	Literal
45	ExprTuple	55, 48
46	Operation	operator: 49 operands: 50
47	ExprRange	lambda_map: 51 start_index: 52 end_index: 53
48	Variable
49	Literal
50	ExprTuple	54, 55
51	Lambda	parameter: 58 body: 55
52	Literal
53	Variable
54	Variable
55	IndexedVar	variable: 56 index: 58
56	Variable
57	ExprTuple	58
58	Variable