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 ExprTuple, K, Lambda, V, m, n
from proveit.linear_algebra import TensorExp, VecSpaces
from proveit.logic import CartExp, Forall, SubsetEq
from proveit.numbers import Mult, NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [m, n], instance_expr = Forall(instance_param_or_params = [V], instance_expr = SubsetEq(TensorExp(CartExp(V, m), n), CartExp(V, Mult(m, n))), domain = VecSpaces(K)), 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, n \in \mathbb{N}^+}~\left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left((V^{m})^{\otimes n} \subseteq V^{m \cdot n}\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: 37 body: 2
2	Operation	operator: 8 operand: 4
3	ExprTuple	4
4	Lambda	parameters: 41 body: 5
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 12
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	13, 14
12	Lambda	parameter: 42 body: 16
13	Operation	operator: 18 operands: 17
14	Operation	operator: 18 operands: 19
15	ExprTuple	42
16	Conditional	value: 20 condition: 21
17	ExprTuple	43, 22
18	Literal
19	ExprTuple	44, 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	Literal
23	Literal
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	42, 29
27	Operation	operator: 30 operands: 31
28	Operation	operator: 38 operands: 32
29	Operation	operator: 33 operand: 37
30	Literal
31	ExprTuple	35, 44
32	ExprTuple	42, 36
33	Literal
34	ExprTuple	37
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operands: 41
37	Variable
38	Literal
39	ExprTuple	42, 43
40	Literal
41	ExprTuple	43, 44
42	Variable
43	Variable
44	Variable