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