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
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, InClass, InSet

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