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 CartExp, Forall, InSet, SubsetEq
from proveit.numbers import Mult, NaturalPos, one

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

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())

m \mapsto \left\{\forall_{n_{1}, n_{2}, \ldots, n_{m} \in \mathbb{N}^+}~\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}}\right) \textrm{ if } m \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 38 body: 2
1	ExprTuple	38
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 29 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	38, 33
8	Lambda	parameters: 28 body: 9
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 34 operands: 21
18	ExprRange	lambda_map: 22 start_index: 37 end_index: 38
19	Literal
20	ExprTuple	23
21	ExprTuple	39, 24
22	Lambda	parameter: 43 body: 25
23	ExprRange	lambda_map: 26 start_index: 37 end_index: 38
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	Lambda	parameter: 43 body: 31
27	Literal
28	ExprTuple	32
29	Literal
30	ExprTuple	40, 33
31	Operation	operator: 34 operands: 35
32	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
33	Literal
34	Literal
35	ExprTuple	39, 40
36	Lambda	parameter: 43 body: 40
37	Literal
38	Variable
39	Variable
40	IndexedVar	variable: 41 index: 43
41	Variable
42	ExprTuple	43
43	Variable