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 Conditional, K, Lambda, V, m, n
from proveit.linear_algebra import TensorExp, VecSpaces
from proveit.logic import CartExp, InClass, SubsetEq
from proveit.numbers import Mult

# build up the expression from sub-expressions
expr = Lambda(V, Conditional(SubsetEq(TensorExp(CartExp(V, m), n), CartExp(V, Mult(m, n))), InClass(V, VecSpaces(K))))

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())

V \mapsto \left\{(V^{m})^{\otimes n} \subseteq V^{m \cdot n} \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\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: 24 body: 2
1	ExprTuple	24
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	24, 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 20 operands: 14
11	Operation	operator: 15 operand: 19
12	Literal
13	ExprTuple	17, 26
14	ExprTuple	24, 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Variable
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	25, 26
24	Variable
25	Variable
26	Variable