Expression of type Conditional

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, V, Variable, a, n
from proveit.core_expr_types import 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 = 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\{\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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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