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 Equals, Forall, InSet
from proveit.numbers import Complex, Natural, one

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

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