Expression of type Lambda

from the theory of proveit.linear_algebra.vector_sets

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
from proveit.linear_algebra import VecZero, lin_comb_axn, some_nonzero_a
from proveit.logic import And, Equals, 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(Equals(lin_comb_axn, VecZero(V)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), K), one, n), some_nonzero_a)))

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\{\left(\left(a_{1} \cdot x_{1}\right) +  \left(a_{2} \cdot x_{2}\right) +  \ldots +  \left(a_{n} \cdot x_{n}\right)\right) = \vec{0}\left(V\right) \textrm{ if } \left(a_{1} \in K\right) ,  \left(a_{2} \in K\right) ,  \ldots ,  \left(a_{n} \in K\right) ,  \left(a_{1} \neq 0\right) \lor  \left(a_{2} \neq 0\right) \lor  \ldots \lor  \left(a_{n} \neq 0\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: 30 end_index: 31
4	Operation	operator: 7 operands: 8
5	Operation	operator: 9 operands: 10
6	Lambda	parameter: 45 body: 40
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 17 operand: 23
13	ExprRange	lambda_map: 19 start_index: 30 end_index: 31
14	Operation	operator: 20 operands: 21
15	Literal
16	ExprTuple	22
17	Literal
18	ExprTuple	23
19	Lambda	parameter: 45 body: 24
20	Literal
21	ExprTuple	25
22	ExprRange	lambda_map: 26 start_index: 30 end_index: 31
23	Variable
24	Operation	operator: 27 operands: 28
25	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
26	Lambda	parameter: 45 body: 32
27	Literal
28	ExprTuple	40, 33
29	Lambda	parameter: 45 body: 34
30	Literal
31	Variable
32	Operation	operator: 35 operands: 36
33	Variable
34	Operation	operator: 37 operands: 38
35	Literal
36	ExprTuple	40, 39
37	Literal
38	ExprTuple	40, 41
39	IndexedVar	variable: 42 index: 45
40	IndexedVar	variable: 43 index: 45
41	Literal
42	Variable
43	Variable
44	ExprTuple	45
45	Variable