Expression of type Conditional

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, IndexedVar, K, 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 = 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(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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 25 operands: 12
9	ExprRange	lambda_map: 13 start_index: 28 end_index: 29
10	Literal
11	ExprTuple	14
12	ExprTuple	30, 15
13	Lambda	parameter: 34 body: 16
14	ExprRange	lambda_map: 17 start_index: 28 end_index: 29
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Lambda	parameter: 34 body: 22
18	Literal
19	ExprTuple	23
20	Literal
21	ExprTuple	31, 24
22	Operation	operator: 25 operands: 26
23	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
24	Literal
25	Literal
26	ExprTuple	30, 31
27	Lambda	parameter: 34 body: 31
28	Literal
29	Variable
30	Variable
31	IndexedVar	variable: 32 index: 34
32	Variable
33	ExprTuple	34
34	Variable