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

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