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, VecSpaces
from proveit.logic import Equals, Forall, InClass
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda(V, Conditional(Forall(instance_param_or_params = [n], instance_expr = 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), domain = Natural), InClass(V, VecSpaces(K)))))

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(V \mapsto \left\{\forall_{n \in \mathbb{N}}~\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]\right] \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(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	parameter: 43 body: 3
2	ExprTuple	43
3	Conditional	value: 4 condition: 5
4	Operation	operator: 24 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	43, 10
9	Lambda	parameter: 56 body: 12
10	Operation	operator: 13 operand: 44
11	ExprTuple	56
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	44
15	Operation	operator: 24 operand: 19
16	Operation	operator: 39 operands: 18
17	ExprTuple	19
18	ExprTuple	56, 20
19	Lambda	parameters: 50 body: 21
20	Literal
21	Conditional	value: 22 condition: 23
22	Operation	operator: 24 operand: 28
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	29
28	Lambda	parameter: 60 body: 31
29	ExprRange	lambda_map: 32 start_index: 55 end_index: 56
30	ExprTuple	60
31	Conditional	value: 33 condition: 34
32	Lambda	parameter: 63 body: 35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 39 operands: 38
35	Operation	operator: 39 operands: 40
36	Literal
37	ExprTuple	41, 42
38	ExprTuple	60, 43
39	Literal
40	ExprTuple	59, 44
41	Operation	operator: 57 operands: 45
42	Operation	operator: 49 operands: 46
43	Variable
44	Variable
45	ExprTuple	47, 60
46	ExprTuple	48
47	Operation	operator: 49 operands: 50
48	ExprRange	lambda_map: 51 start_index: 55 end_index: 56
49	Literal
50	ExprTuple	52
51	Lambda	parameter: 63 body: 53
52	ExprRange	lambda_map: 54 start_index: 55 end_index: 56
53	Operation	operator: 57 operands: 58
54	Lambda	parameter: 63 body: 59
55	Literal
56	Variable
57	Literal
58	ExprTuple	59, 60
59	IndexedVar	variable: 61 index: 63
60	Variable
61	Variable
62	ExprTuple	63
63	Variable