Expression of type Lambda

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, Lambda, 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 = Lambda([a_1_to_i, v], 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(a_{1}, a_{2}, \ldots, a_{i}, v\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

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