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 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 = ExprTuple(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())

\left(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..\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	parameter: 39 body: 3
2	ExprTuple	39
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 30 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	39, 34
9	Lambda	parameters: 29 body: 10
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 35 operands: 22
19	ExprRange	lambda_map: 23 start_index: 38 end_index: 39
20	Literal
21	ExprTuple	24
22	ExprTuple	40, 25
23	Lambda	parameter: 44 body: 26
24	ExprRange	lambda_map: 27 start_index: 38 end_index: 39
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	Lambda	parameter: 44 body: 32
28	Literal
29	ExprTuple	33
30	Literal
31	ExprTuple	41, 34
32	Operation	operator: 35 operands: 36
33	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
34	Literal
35	Literal
36	ExprTuple	40, 41
37	Lambda	parameter: 44 body: 41
38	Literal
39	Variable
40	Variable
41	IndexedVar	variable: 42 index: 44
42	Variable
43	ExprTuple	44
44	Variable