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, 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 = ExprTuple(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(\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..\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: 31 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10
9	Lambda	parameter: 41 body: 12
10	ExprRange	lambda_map: 13 start_index: 36 end_index: 37
11	ExprTuple	41
12	Conditional	value: 14 condition: 15
13	Lambda	parameter: 44 body: 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 20 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	ExprTuple	22, 23
19	ExprTuple	41, 24
20	Literal
21	ExprTuple	40, 25
22	Operation	operator: 38 operands: 26
23	Operation	operator: 30 operands: 27
24	Variable
25	Variable
26	ExprTuple	28, 41
27	ExprTuple	29
28	Operation	operator: 30 operands: 31
29	ExprRange	lambda_map: 32 start_index: 36 end_index: 37
30	Literal
31	ExprTuple	33
32	Lambda	parameter: 44 body: 34
33	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
34	Operation	operator: 38 operands: 39
35	Lambda	parameter: 44 body: 40
36	Literal
37	Variable
38	Literal
39	ExprTuple	40, 41
40	IndexedVar	variable: 42 index: 44
41	Variable
42	Variable
43	ExprTuple	44
44	Variable