Expression of type ExprTuple

from the theory of proveit.linear_algebra.tensors

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, i
from proveit.core_expr_types import V_1_to_i, a_1_to_i
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import And, Forall, InClass, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [V_1_to_i]
expr = ExprTuple(Lambda(sub_expr2, Conditional(Forall(instance_param_or_params = [a_1_to_i], instance_expr = InSet(TensorProd(a_1_to_i), TensorProd(V_1_to_i)), domains = sub_expr2), And(ExprRange(sub_expr1, InClass(IndexedVar(V, sub_expr1), VecSpaces(K)), one, i)))))

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