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, Variable, m, n
from proveit.core_expr_types import n_1_to_m
from proveit.linear_algebra import TensorProd
from proveit.logic import And, CartExp, InSet, SubsetEq
from proveit.numbers import Mult, NaturalPos, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(n, sub_expr1)
expr = ExprTuple(Lambda([n_1_to_m], Conditional(SubsetEq(TensorProd(ExprRange(sub_expr1, CartExp(K, sub_expr2), one, m)), CartExp(K, Mult(n_1_to_m))), And(ExprRange(sub_expr1, InSet(sub_expr2, NaturalPos), one, m)))))

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(n_{1}, n_{2}, \ldots, n_{m}\right) \mapsto \left\{\left(K^{n_{1}} {\otimes}  K^{n_{2}} {\otimes}  \ldots {\otimes}  K^{n_{m}}\right) \subseteq K^{n_{1} \cdot  n_{2} \cdot  \ldots \cdot  n_{m}} \textrm{ if } \left(n_{1} \in \mathbb{N}^+\right) \land  \left(n_{2} \in \mathbb{N}^+\right) \land  \ldots \land  \left(n_{m} \in \mathbb{N}^+\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: 21 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 27 operands: 14
11	ExprRange	lambda_map: 15 start_index: 30 end_index: 31
12	Literal
13	ExprTuple	16
14	ExprTuple	32, 17
15	Lambda	parameter: 36 body: 18
16	ExprRange	lambda_map: 19 start_index: 30 end_index: 31
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Lambda	parameter: 36 body: 24
20	Literal
21	ExprTuple	25
22	Literal
23	ExprTuple	33, 26
24	Operation	operator: 27 operands: 28
25	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
26	Literal
27	Literal
28	ExprTuple	32, 33
29	Lambda	parameter: 36 body: 33
30	Literal
31	Variable
32	Variable
33	IndexedVar	variable: 34 index: 36
34	Variable
35	ExprTuple	36
36	Variable