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, v
from proveit.core_expr_types import a_1_to_n
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(a, sub_expr1)
expr = Conditional(Forall(instance_param_or_params = [v], instance_expr = Equals(ScalarMult(VecAdd(a_1_to_n), v), VecAdd(ExprRange(sub_expr1, ScalarMult(sub_expr2, v), one, n))).with_wrapping_at(2), domain = V), And(ExprRange(sub_expr1, InSet(sub_expr2, 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_{v \in V}~\left(\begin{array}{c} \begin{array}{l} \left(\left(a_{1} +  a_{2} +  \ldots +  a_{n}\right) \cdot v\right) =  \\ \left(\left(a_{1} \cdot v\right) +  \left(a_{2} \cdot v\right) +  \ldots +  \left(a_{n} \cdot v\right)\right) \end{array} \end{array}\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: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8
7	Lambda	parameter: 39 body: 10
8	ExprRange	lambda_map: 11 start_index: 34 end_index: 35
9	ExprTuple	39
10	Conditional	value: 12 condition: 13
11	Lambda	parameter: 42 body: 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 18 operands: 17
14	Operation	operator: 18 operands: 19
15	Literal
16	ExprTuple	20, 21
17	ExprTuple	39, 22
18	Literal
19	ExprTuple	38, 23
20	Operation	operator: 36 operands: 24
21	Operation	operator: 28 operands: 25
22	Variable
23	Variable
24	ExprTuple	26, 39
25	ExprTuple	27
26	Operation	operator: 28 operands: 29
27	ExprRange	lambda_map: 30 start_index: 34 end_index: 35
28	Literal
29	ExprTuple	31
30	Lambda	parameter: 42 body: 32
31	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
32	Operation	operator: 36 operands: 37
33	Lambda	parameter: 42 body: 38
34	Literal
35	Variable
36	Literal
37	ExprTuple	38, 39
38	IndexedVar	variable: 40 index: 42
39	Variable
40	Variable
41	ExprTuple	42
42	Variable