Expression of type ExprTuple

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, ExprTuple, IndexedVar, K, Lambda, V, Variable, a, i, k
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 one

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

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(\left(k, a_{1}, a_{2}, \ldots, a_{i}\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(\left(k \cdot a_{1}\right) +  \left(k \cdot a_{2}\right) +  \ldots +  \left(k \cdot a_{i}\right)\right) =  \\ \left(k \cdot \left(a_{1} +  a_{2} +  \ldots +  a_{i}\right)\right) \end{array} \end{array} \textrm{ if } k \in K, \left(a_{1} \in V\right) ,  \left(a_{2} \in V\right) ,  \ldots ,  \left(a_{i} \in V\right)\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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