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 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
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [V], instance_expr = 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), domain = 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(K \mapsto \left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\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]\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: 47 body: 2
2	Operation	operator: 27 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 46 body: 6
5	ExprTuple	46
6	Conditional	value: 7 condition: 8
7	Operation	operator: 27 operand: 12
8	Operation	operator: 10 operands: 11
9	ExprTuple	12
10	Literal
11	ExprTuple	46, 13
12	Lambda	parameter: 59 body: 15
13	Operation	operator: 16 operand: 47
14	ExprTuple	59
15	Conditional	value: 18 condition: 19
16	Literal
17	ExprTuple	47
18	Operation	operator: 27 operand: 22
19	Operation	operator: 42 operands: 21
20	ExprTuple	22
21	ExprTuple	59, 23
22	Lambda	parameters: 53 body: 24
23	Literal
24	Conditional	value: 25 condition: 26
25	Operation	operator: 27 operand: 31
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	31
29	Literal
30	ExprTuple	32
31	Lambda	parameter: 63 body: 34
32	ExprRange	lambda_map: 35 start_index: 58 end_index: 59
33	ExprTuple	63
34	Conditional	value: 36 condition: 37
35	Lambda	parameter: 66 body: 38
36	Operation	operator: 39 operands: 40
37	Operation	operator: 42 operands: 41
38	Operation	operator: 42 operands: 43
39	Literal
40	ExprTuple	44, 45
41	ExprTuple	63, 46
42	Literal
43	ExprTuple	62, 47
44	Operation	operator: 60 operands: 48
45	Operation	operator: 52 operands: 49
46	Variable
47	Variable
48	ExprTuple	50, 63
49	ExprTuple	51
50	Operation	operator: 52 operands: 53
51	ExprRange	lambda_map: 54 start_index: 58 end_index: 59
52	Literal
53	ExprTuple	55
54	Lambda	parameter: 66 body: 56
55	ExprRange	lambda_map: 57 start_index: 58 end_index: 59
56	Operation	operator: 60 operands: 61
57	Lambda	parameter: 66 body: 62
58	Literal
59	Variable
60	Literal
61	ExprTuple	62, 63
62	IndexedVar	variable: 64 index: 66
63	Variable
64	Variable
65	ExprTuple	66
66	Variable