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, n
from proveit.core_expr_types import a_1_to_n, x_1_to_n
from proveit.linear_algebra import VecSpaces, lin_comb_axn
from proveit.logic import Forall, InSet
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [K], instance_expr = Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [a_1_to_n], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = InSet(lin_comb_axn, V), domain = V), domain = K), domain = VecSpaces(K))), InSet(n, NaturalPos)))

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())

n \mapsto \left\{\forall_{K}~\left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{n} \in K}~\left[\forall_{x_{1}, x_{2}, \ldots, x_{n} \in V}~\left(\left(\left(a_{1} \cdot x_{1}\right) +  \left(a_{2} \cdot x_{2}\right) +  \ldots +  \left(a_{n} \cdot x_{n}\right)\right) \in V\right)\right]\right]\right] \textrm{ if } n \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 56 body: 2
1	ExprTuple	56
2	Conditional	value: 3 condition: 4
3	Operation	operator: 29 operand: 7
4	Operation	operator: 57 operands: 6
5	ExprTuple	7
6	ExprTuple	56, 8
7	Lambda	parameter: 48 body: 9
8	Literal
9	Operation	operator: 29 operand: 11
10	ExprTuple	11
11	Lambda	parameter: 60 body: 13
12	ExprTuple	60
13	Conditional	value: 14 condition: 15
14	Operation	operator: 29 operand: 19
15	Operation	operator: 17 operands: 18
16	ExprTuple	19
17	Literal
18	ExprTuple	60, 20
19	Lambda	parameters: 21 body: 22
20	Operation	operator: 23 operand: 48
21	ExprTuple	25
22	Conditional	value: 26 condition: 27
23	Literal
24	ExprTuple	48
25	ExprRange	lambda_map: 28 start_index: 55 end_index: 56
26	Operation	operator: 29 operand: 32
27	Operation	operator: 43 operands: 31
28	Lambda	parameter: 68 body: 63
29	Literal
30	ExprTuple	32
31	ExprTuple	33
32	Lambda	parameters: 34 body: 35
33	ExprRange	lambda_map: 36 start_index: 55 end_index: 56
34	ExprTuple	37
35	Conditional	value: 38 condition: 39
36	Lambda	parameter: 68 body: 40
37	ExprRange	lambda_map: 41 start_index: 55 end_index: 56
38	Operation	operator: 57 operands: 42
39	Operation	operator: 43 operands: 44
40	Operation	operator: 57 operands: 45
41	Lambda	parameter: 68 body: 64
42	ExprTuple	46, 60
43	Literal
44	ExprTuple	47
45	ExprTuple	63, 48
46	Operation	operator: 49 operands: 50
47	ExprRange	lambda_map: 51 start_index: 55 end_index: 56
48	Variable
49	Literal
50	ExprTuple	52
51	Lambda	parameter: 68 body: 53
52	ExprRange	lambda_map: 54 start_index: 55 end_index: 56
53	Operation	operator: 57 operands: 58
54	Lambda	parameter: 68 body: 59
55	Literal
56	Variable
57	Literal
58	ExprTuple	64, 60
59	Operation	operator: 61 operands: 62
60	Variable
61	Literal
62	ExprTuple	63, 64
63	IndexedVar	variable: 65 index: 68
64	IndexedVar	variable: 66 index: 68
65	Variable
66	Variable
67	ExprTuple	68
68	Variable