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, x
from proveit.core_expr_types import x_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], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(ScalarMult(a, VecAdd(x_1_to_n)), VecAdd(ExprRange(sub_expr1, ScalarMult(a, IndexedVar(x, sub_expr1)), 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 \in K}~\left[\forall_{x_{1}, x_{2}, \ldots, x_{n} \in V}~\left(\begin{array}{c} \begin{array}{l} \left(a \cdot \left(x_{1} +  x_{2} +  \ldots +  x_{n}\right)\right) =  \\ \left(\left(a \cdot x_{1}\right) +  \left(a \cdot x_{2}\right) +  \ldots +  \left(a \cdot x_{n}\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: 32 body: 2
2	Operation	operator: 28 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 56 body: 6
5	ExprTuple	56
6	Conditional	value: 7 condition: 8
7	Operation	operator: 28 operand: 12
8	Operation	operator: 10 operands: 11
9	ExprTuple	12
10	Literal
11	ExprTuple	56, 13
12	Lambda	parameter: 59 body: 15
13	Operation	operator: 16 operand: 32
14	ExprTuple	59
15	Conditional	value: 18 condition: 19
16	Literal
17	ExprTuple	32
18	Operation	operator: 28 operand: 22
19	Operation	operator: 52 operands: 21
20	ExprTuple	22
21	ExprTuple	59, 23
22	Lambda	parameter: 62 body: 25
23	Literal
24	ExprTuple	62
25	Conditional	value: 26 condition: 27
26	Operation	operator: 28 operand: 31
27	Operation	operator: 52 operands: 30
28	Literal
29	ExprTuple	31
30	ExprTuple	62, 32
31	Lambda	parameters: 50 body: 33
32	Variable
33	Conditional	value: 34 condition: 35
34	Operation	operator: 36 operands: 37
35	Operation	operator: 38 operands: 39
36	Literal
37	ExprTuple	40, 41
38	Literal
39	ExprTuple	42
40	Operation	operator: 60 operands: 43
41	Operation	operator: 49 operands: 44
42	ExprRange	lambda_map: 45 start_index: 58 end_index: 59
43	ExprTuple	62, 46
44	ExprTuple	47
45	Lambda	parameter: 66 body: 48
46	Operation	operator: 49 operands: 50
47	ExprRange	lambda_map: 51 start_index: 58 end_index: 59
48	Operation	operator: 52 operands: 53
49	Literal
50	ExprTuple	54
51	Lambda	parameter: 66 body: 55
52	Literal
53	ExprTuple	63, 56
54	ExprRange	lambda_map: 57 start_index: 58 end_index: 59
55	Operation	operator: 60 operands: 61
56	Variable
57	Lambda	parameter: 66 body: 63
58	Literal
59	Variable
60	Literal
61	ExprTuple	62, 63
62	Variable
63	IndexedVar	variable: 64 index: 66
64	Variable
65	ExprTuple	66
66	Variable