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, i, v
from proveit.core_expr_types import a_1_to_i
from proveit.linear_algebra import ScalarMult, VecAdd, VecSpaces
from proveit.logic import Equals, Forall
from proveit.numbers import Complex, 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 = [i], instance_expr = Forall(instance_param_or_params = [a_1_to_i, v], instance_expr = Equals(VecAdd(ExprRange(sub_expr1, ScalarMult(IndexedVar(a, sub_expr1), v), one, i)), ScalarMult(VecAdd(a_1_to_i), v)).with_wrapping_at(2), domains = [Complex, V]), 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_{i \in \mathbb{N}}~\left[\forall_{\left(a_{1} \in \mathbb{C}\right), \left(a_{2} \in \mathbb{C}\right), \ldots, \left(a_{i} \in \mathbb{C}\right), v \in V}~\left(\begin{array}{c} \begin{array}{l} \left(\left(a_{1} \cdot v\right) +  \left(a_{2} \cdot v\right) +  \ldots +  \left(a_{i} \cdot v\right)\right) =  \\ \left(\left(a_{1} +  a_{2} +  \ldots +  a_{i}\right) \cdot v\right) \end{array} \end{array}\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: 20 body: 2
2	Operation	operator: 21 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 45 body: 6
5	ExprTuple	45
6	Conditional	value: 7 condition: 8
7	Operation	operator: 21 operand: 12
8	Operation	operator: 10 operands: 11
9	ExprTuple	12
10	Literal
11	ExprTuple	45, 13
12	Lambda	parameter: 58 body: 15
13	Operation	operator: 16 operand: 20
14	ExprTuple	58
15	Conditional	value: 18 condition: 19
16	Literal
17	ExprTuple	20
18	Operation	operator: 21 operand: 24
19	Operation	operator: 49 operands: 23
20	Variable
21	Literal
22	ExprTuple	24
23	ExprTuple	58, 25
24	Lambda	parameters: 26 body: 27
25	Literal
26	ExprTuple	52, 59
27	Conditional	value: 28 condition: 29
28	Operation	operator: 30 operands: 31
29	Operation	operator: 32 operands: 33
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36, 37
34	Operation	operator: 47 operands: 38
35	Operation	operator: 54 operands: 39
36	ExprRange	lambda_map: 40 start_index: 57 end_index: 58
37	Operation	operator: 49 operands: 41
38	ExprTuple	42
39	ExprTuple	43, 59
40	Lambda	parameter: 63 body: 44
41	ExprTuple	59, 45
42	ExprRange	lambda_map: 46 start_index: 57 end_index: 58
43	Operation	operator: 47 operands: 48
44	Operation	operator: 49 operands: 50
45	Variable
46	Lambda	parameter: 63 body: 51
47	Literal
48	ExprTuple	52
49	Literal
50	ExprTuple	60, 53
51	Operation	operator: 54 operands: 55
52	ExprRange	lambda_map: 56 start_index: 57 end_index: 58
53	Literal
54	Literal
55	ExprTuple	60, 59
56	Lambda	parameter: 63 body: 60
57	Literal
58	Variable
59	Variable
60	IndexedVar	variable: 61 index: 63
61	Variable
62	ExprTuple	63
63	Variable