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, n
from proveit.linear_algebra import TensorExp, VecSpaces
from proveit.logic import CartExp, Forall, SubsetEq
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Lambda(K, Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [V], instance_expr = SubsetEq(TensorExp(V, n), CartExp(V, 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_{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()

no style options

# display the expression information
stored_expr.expr_info()

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