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
from proveit.core_expr_types import a_1_to_n, x_1_to_n
from proveit.linear_algebra import lin_comb_axn
from proveit.logic import And, 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_1_to_n], Conditional(Forall(instance_param_or_params = [x_1_to_n], instance_expr = InSet(lin_comb_axn, V), domain = V), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), K), one, n)))))

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(\left(a_{1}, a_{2}, \ldots, a_{n}\right) \mapsto \left\{\forall_{x_{1}, x_{2}, \ldots, x_{n} \in V}~\left(\left(\left(a_{1} \cdot x_{1}\right) +  \left(a_{2} \cdot x_{2}\right) +  \ldots +  \left(a_{n} \cdot x_{n}\right)\right) \in V\right) \textrm{ if } \left(a_{1} \in K\right) \land  \left(a_{2} \in K\right) \land  \ldots \land  \left(a_{n} \in 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	parameters: 2 body: 3
2	ExprTuple	4
3	Conditional	value: 5 condition: 6
4	ExprRange	lambda_map: 7 start_index: 34 end_index: 35
5	Operation	operator: 8 operand: 11
6	Operation	operator: 22 operands: 10
7	Lambda	parameter: 47 body: 42
8	Literal
9	ExprTuple	11
10	ExprTuple	12
11	Lambda	parameters: 13 body: 14
12	ExprRange	lambda_map: 15 start_index: 34 end_index: 35
13	ExprTuple	16
14	Conditional	value: 17 condition: 18
15	Lambda	parameter: 47 body: 19
16	ExprRange	lambda_map: 20 start_index: 34 end_index: 35
17	Operation	operator: 36 operands: 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 36 operands: 24
20	Lambda	parameter: 47 body: 43
21	ExprTuple	25, 39
22	Literal
23	ExprTuple	26
24	ExprTuple	42, 27
25	Operation	operator: 28 operands: 29
26	ExprRange	lambda_map: 30 start_index: 34 end_index: 35
27	Variable
28	Literal
29	ExprTuple	31
30	Lambda	parameter: 47 body: 32
31	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
32	Operation	operator: 36 operands: 37
33	Lambda	parameter: 47 body: 38
34	Literal
35	Variable
36	Literal
37	ExprTuple	43, 39
38	Operation	operator: 40 operands: 41
39	Variable
40	Literal
41	ExprTuple	42, 43
42	IndexedVar	variable: 44 index: 47
43	IndexedVar	variable: 45 index: 47
44	Variable
45	Variable
46	ExprTuple	47
47	Variable