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

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda(a, Conditional(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), InSet(a, 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(a \mapsto \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) \textrm{ if } a \in K\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: 40 body: 3
2	ExprTuple	40
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 30 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	40, 10
9	Lambda	parameters: 28 body: 11
10	Variable
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20
18	Operation	operator: 38 operands: 21
19	Operation	operator: 27 operands: 22
20	ExprRange	lambda_map: 23 start_index: 36 end_index: 37
21	ExprTuple	40, 24
22	ExprTuple	25
23	Lambda	parameter: 44 body: 26
24	Operation	operator: 27 operands: 28
25	ExprRange	lambda_map: 29 start_index: 36 end_index: 37
26	Operation	operator: 30 operands: 31
27	Literal
28	ExprTuple	32
29	Lambda	parameter: 44 body: 33
30	Literal
31	ExprTuple	41, 34
32	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
33	Operation	operator: 38 operands: 39
34	Variable
35	Lambda	parameter: 44 body: 41
36	Literal
37	Variable
38	Literal
39	ExprTuple	40, 41
40	Variable
41	IndexedVar	variable: 42 index: 44
42	Variable
43	ExprTuple	44
44	Variable