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