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 Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [a], instance_expr = 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), domain = K), InSet(n, 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(n \mapsto \left\{\forall_{a \in K}~\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)\right] \textrm{ if } n \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: 45 body: 3
2	ExprTuple	45
3	Conditional	value: 4 condition: 5
4	Operation	operator: 14 operand: 8
5	Operation	operator: 38 operands: 7
6	ExprTuple	8
7	ExprTuple	45, 9
8	Lambda	parameter: 48 body: 11
9	Literal
10	ExprTuple	48
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operand: 17
13	Operation	operator: 38 operands: 16
14	Literal
15	ExprTuple	17
16	ExprTuple	48, 18
17	Lambda	parameters: 36 body: 19
18	Variable
19	Conditional	value: 20 condition: 21
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28
26	Operation	operator: 46 operands: 29
27	Operation	operator: 35 operands: 30
28	ExprRange	lambda_map: 31 start_index: 44 end_index: 45
29	ExprTuple	48, 32
30	ExprTuple	33
31	Lambda	parameter: 52 body: 34
32	Operation	operator: 35 operands: 36
33	ExprRange	lambda_map: 37 start_index: 44 end_index: 45
34	Operation	operator: 38 operands: 39
35	Literal
36	ExprTuple	40
37	Lambda	parameter: 52 body: 41
38	Literal
39	ExprTuple	49, 42
40	ExprRange	lambda_map: 43 start_index: 44 end_index: 45
41	Operation	operator: 46 operands: 47
42	Variable
43	Lambda	parameter: 52 body: 49
44	Literal
45	Variable
46	Literal
47	ExprTuple	48, 49
48	Variable
49	IndexedVar	variable: 50 index: 52
50	Variable
51	ExprTuple	52
52	Variable