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
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda(i, Conditional(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]), InSet(i, Natural))))

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(i \mapsto \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) \textrm{ if } i \in \mathbb{N}\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: 43 body: 3
2	ExprTuple	43
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 34 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	43, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	44, 37
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 32 operands: 23
20	Operation	operator: 39 operands: 24
21	Operation	operator: 34 operands: 25
22	ExprRange	lambda_map: 26 start_index: 42 end_index: 43
23	ExprTuple	27
24	ExprTuple	44, 28
25	ExprTuple	44, 29
26	Lambda	parameter: 48 body: 30
27	ExprRange	lambda_map: 31 start_index: 42 end_index: 43
28	Operation	operator: 32 operands: 33
29	Variable
30	Operation	operator: 34 operands: 35
31	Lambda	parameter: 48 body: 36
32	Literal
33	ExprTuple	37
34	Literal
35	ExprTuple	45, 38
36	Operation	operator: 39 operands: 40
37	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
38	Variable
39	Literal
40	ExprTuple	44, 45
41	Lambda	parameter: 48 body: 45
42	Literal
43	Variable
44	Variable
45	IndexedVar	variable: 46 index: 48
46	Variable
47	ExprTuple	48
48	Variable