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, n
from proveit.core_expr_types import a_1_to_n, x_1_to_n
from proveit.linear_algebra import lin_comb_axn
from proveit.logic import And, Forall, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_n], Conditional(Forall(instance_param_or_params = [x_1_to_n], instance_expr = InSet(lin_comb_axn, V), domain = V), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), K), one, n))))

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())

\left(a_{1}, a_{2}, \ldots, a_{n}\right) \mapsto \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) \textrm{ if } \left(a_{1} \in K\right) \land  \left(a_{2} \in K\right) \land  \ldots \land  \left(a_{n} \in 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	parameters: 1 body: 2
1	ExprTuple	3
2	Conditional	value: 4 condition: 5
3	ExprRange	lambda_map: 6 start_index: 33 end_index: 34
4	Operation	operator: 7 operand: 10
5	Operation	operator: 21 operands: 9
6	Lambda	parameter: 46 body: 41
7	Literal
8	ExprTuple	10
9	ExprTuple	11
10	Lambda	parameters: 12 body: 13
11	ExprRange	lambda_map: 14 start_index: 33 end_index: 34
12	ExprTuple	15
13	Conditional	value: 16 condition: 17
14	Lambda	parameter: 46 body: 18
15	ExprRange	lambda_map: 19 start_index: 33 end_index: 34
16	Operation	operator: 35 operands: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 35 operands: 23
19	Lambda	parameter: 46 body: 42
20	ExprTuple	24, 38
21	Literal
22	ExprTuple	25
23	ExprTuple	41, 26
24	Operation	operator: 27 operands: 28
25	ExprRange	lambda_map: 29 start_index: 33 end_index: 34
26	Variable
27	Literal
28	ExprTuple	30
29	Lambda	parameter: 46 body: 31
30	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
31	Operation	operator: 35 operands: 36
32	Lambda	parameter: 46 body: 37
33	Literal
34	Variable
35	Literal
36	ExprTuple	42, 38
37	Operation	operator: 39 operands: 40
38	Variable
39	Literal
40	ExprTuple	41, 42
41	IndexedVar	variable: 43 index: 46
42	IndexedVar	variable: 44 index: 46
43	Variable
44	Variable
45	ExprTuple	46
46	Variable