Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 20 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 26 operands: 13
10	ExprRange	lambda_map: 14 start_index: 29 end_index: 30
11	Literal
12	ExprTuple	15
13	ExprTuple	31, 16
14	Lambda	parameter: 35 body: 17
15	ExprRange	lambda_map: 18 start_index: 29 end_index: 30
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Lambda	parameter: 35 body: 23
19	Literal
20	ExprTuple	24
21	Literal
22	ExprTuple	32, 25
23	Operation	operator: 26 operands: 27
24	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
25	Literal
26	Literal
27	ExprTuple	31, 32
28	Lambda	parameter: 35 body: 32
29	Literal
30	Variable
31	Variable
32	IndexedVar	variable: 33 index: 35
33	Variable
34	ExprTuple	35
35	Variable