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

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = Forall(instance_param_or_params = [v], instance_expr = Equals(ScalarMult(VecAdd(a_1_to_n), v), VecAdd(ExprRange(sub_expr1, ScalarMult(IndexedVar(a, sub_expr1), v), one, n))).with_wrapping_at(2), domain = V), domain = K), InSet(n, 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(n \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{n} \in K}~\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)\right] \textrm{ if } n \in \mathbb{N}\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	parameter: 45 body: 3
2	ExprTuple	45
3	Conditional	value: 4 condition: 5
4	Operation	operator: 13 operand: 8
5	Operation	operator: 28 operands: 7
6	ExprTuple	8
7	ExprTuple	45, 9
8	Lambda	parameters: 39 body: 10
9	Literal
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operand: 17
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17
15	Literal
16	ExprTuple	18
17	Lambda	parameter: 49 body: 20
18	ExprRange	lambda_map: 21 start_index: 44 end_index: 45
19	ExprTuple	49
20	Conditional	value: 22 condition: 23
21	Lambda	parameter: 52 body: 24
22	Operation	operator: 25 operands: 26
23	Operation	operator: 28 operands: 27
24	Operation	operator: 28 operands: 29
25	Literal
26	ExprTuple	30, 31
27	ExprTuple	49, 32
28	Literal
29	ExprTuple	48, 33
30	Operation	operator: 46 operands: 34
31	Operation	operator: 38 operands: 35
32	Variable
33	Variable
34	ExprTuple	36, 49
35	ExprTuple	37
36	Operation	operator: 38 operands: 39
37	ExprRange	lambda_map: 40 start_index: 44 end_index: 45
38	Literal
39	ExprTuple	41
40	Lambda	parameter: 52 body: 42
41	ExprRange	lambda_map: 43 start_index: 44 end_index: 45
42	Operation	operator: 46 operands: 47
43	Lambda	parameter: 52 body: 48
44	Literal
45	Variable
46	Literal
47	ExprTuple	48, 49
48	IndexedVar	variable: 50 index: 52
49	Variable
50	Variable
51	ExprTuple	52
52	Variable