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