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, V, Variable, a, i, v
from proveit.core_expr_types import a_1_to_i
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(a, sub_expr1)
expr = Conditional(Equals(VecAdd(ExprRange(sub_expr1, ScalarMult(sub_expr2, v), one, i)), ScalarMult(VecAdd(a_1_to_i), v)).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(sub_expr2, Complex), one, i), InSet(v, V)))

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\{\begin{array}{c} \begin{array}{l} \left(\left(a_{1} \cdot v\right) +  \left(a_{2} \cdot v\right) +  \ldots +  \left(a_{i} \cdot v\right)\right) =  \\ \left(\left(a_{1} +  a_{2} +  \ldots +  a_{i}\right) \cdot v\right) \end{array} \end{array} \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{C}\right) ,  v \in V\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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 20 operands: 11
8	Operation	operator: 27 operands: 12
9	ExprRange	lambda_map: 13 start_index: 30 end_index: 31
10	Operation	operator: 22 operands: 14
11	ExprTuple	15
12	ExprTuple	16, 32
13	Lambda	parameter: 36 body: 17
14	ExprTuple	32, 18
15	ExprRange	lambda_map: 19 start_index: 30 end_index: 31
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operands: 23
18	Variable
19	Lambda	parameter: 36 body: 24
20	Literal
21	ExprTuple	25
22	Literal
23	ExprTuple	33, 26
24	Operation	operator: 27 operands: 28
25	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
26	Literal
27	Literal
28	ExprTuple	33, 32
29	Lambda	parameter: 36 body: 33
30	Literal
31	Variable
32	Variable
33	IndexedVar	variable: 34 index: 36
34	Variable
35	ExprTuple	36
36	Variable