Theorem tensor_exp_inclusion of type Forall

from the theory of proveit.linear_algebra.tensors

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.linear_algebra.tensors import tensor_exp_inclusion

# check that the built expression is the same as the stored expression
assert tensor_exp_inclusion.expr == stored_expr
assert tensor_exp_inclusion.expr._style_id == stored_expr._style_id
print("Passed sanity check: tensor_exp_inclusion matches stored_expr")

Passed sanity check: tensor_exp_inclusion matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{K}~\left[\forall_{n \in \mathbb{N}^+}~\left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left(V^{\otimes n} \subseteq V^{n}\right)\right]\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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