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, K, Lambda, 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 = Lambda([a_1_to_n], 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(a_{1}, a_{2}, \ldots, a_{n}\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 30 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 8
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Lambda	parameter: 40 body: 11
9	ExprRange	lambda_map: 12 start_index: 35 end_index: 36
10	ExprTuple	40
11	Conditional	value: 13 condition: 14
12	Lambda	parameter: 43 body: 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 19 operands: 18
15	Operation	operator: 19 operands: 20
16	Literal
17	ExprTuple	21, 22
18	ExprTuple	40, 23
19	Literal
20	ExprTuple	39, 24
21	Operation	operator: 37 operands: 25
22	Operation	operator: 29 operands: 26
23	Variable
24	Variable
25	ExprTuple	27, 40
26	ExprTuple	28
27	Operation	operator: 29 operands: 30
28	ExprRange	lambda_map: 31 start_index: 35 end_index: 36
29	Literal
30	ExprTuple	32
31	Lambda	parameter: 43 body: 33
32	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
33	Operation	operator: 37 operands: 38
34	Lambda	parameter: 43 body: 39
35	Literal
36	Variable
37	Literal
38	ExprTuple	39, 40
39	IndexedVar	variable: 41 index: 43
40	Variable
41	Variable
42	ExprTuple	43
43	Variable