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 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, 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(K, Forall(instance_param_or_params = [m], instance_expr = 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), domain = 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(K \mapsto \left[\forall_{m \in \mathbb{N}^+}~\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)\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	parameter: 44 body: 3
2	ExprTuple	44
3	Operation	operator: 10 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 43 body: 7
6	ExprTuple	43
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 13
9	Operation	operator: 34 operands: 12
10	Literal
11	ExprTuple	13
12	ExprTuple	43, 38
13	Lambda	parameters: 33 body: 14
14	Conditional	value: 15 condition: 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23
21	Operation	operator: 24 operands: 25
22	Operation	operator: 39 operands: 26
23	ExprRange	lambda_map: 27 start_index: 42 end_index: 43
24	Literal
25	ExprTuple	28
26	ExprTuple	44, 29
27	Lambda	parameter: 48 body: 30
28	ExprRange	lambda_map: 31 start_index: 42 end_index: 43
29	Operation	operator: 32 operands: 33
30	Operation	operator: 34 operands: 35
31	Lambda	parameter: 48 body: 36
32	Literal
33	ExprTuple	37
34	Literal
35	ExprTuple	45, 38
36	Operation	operator: 39 operands: 40
37	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
38	Literal
39	Literal
40	ExprTuple	44, 45
41	Lambda	parameter: 48 body: 45
42	Literal
43	Variable
44	Variable
45	IndexedVar	variable: 46 index: 48
46	Variable
47	ExprTuple	48
48	Variable