Expression of type Lambda

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 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 = 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())

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]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 36 body: 1
1	Operation	operator: 7 operand: 3
2	ExprTuple	3
3	Lambda	parameters: 40 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	12, 13
11	Lambda	parameter: 41 body: 15
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	41
15	Conditional	value: 19 condition: 20
16	ExprTuple	42, 21
17	Literal
18	ExprTuple	43, 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Literal
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	41, 28
26	Operation	operator: 29 operands: 30
27	Operation	operator: 37 operands: 31
28	Operation	operator: 32 operand: 36
29	Literal
30	ExprTuple	34, 43
31	ExprTuple	41, 35
32	Literal
33	ExprTuple	36
34	Operation	operator: 37 operands: 38
35	Operation	operator: 39 operands: 40
36	Variable
37	Literal
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	42, 43
41	Variable
42	Variable
43	Variable