Expression of type Conditional ¶

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, 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 = 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)))

# 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\{\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..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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

Expression of type Conditional¶

from the theory of proveit.linear_algebra.tensors¶

Expression of type Conditional ¶

from the theory of proveit.linear_algebra.tensors ¶