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 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, InSet

# build up the expression from sub-expressions
expr = Lambda(K, 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)))

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_{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]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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