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 A, B, Conditional, K, U, V, W
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import And, Exists, Forall, InClass, InSet

# build up the expression from sub-expressions
sub_expr1 = VecSpaces(K)
expr = Conditional(Forall(instance_param_or_params = [A, B], instance_expr = Exists(instance_param_or_params = [U, V], instance_expr = And(InSet(A, U), InSet(B, V)), domain = sub_expr1), condition = InSet(TensorProd(A, B), W)), InClass(W, sub_expr1))

# 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_{A, B~|~\left(A {\otimes} B\right) \in W}~\left[\exists_{U, V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left(\left(A \in U\right) \land \left(B \in V\right)\right)\right] \textrm{ if } W \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\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: 6
2	Operation	operator: 33 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	15, 39
6	Lambda	parameters: 19 body: 7
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 13
9	Operation	operator: 30 operands: 12
10	Literal
11	ExprTuple	13
12	ExprTuple	14, 15
13	Lambda	parameters: 16 body: 17
14	Operation	operator: 18 operands: 19
15	Variable
16	ExprTuple	37, 38
17	Conditional	value: 20 condition: 21
18	Literal
19	ExprTuple	35, 36
20	Operation	operator: 23 operands: 22
21	Operation	operator: 23 operands: 24
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27, 28
25	Operation	operator: 30 operands: 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 33 operands: 32
28	Operation	operator: 33 operands: 34
29	ExprTuple	35, 37
30	Literal
31	ExprTuple	36, 38
32	ExprTuple	37, 39
33	Literal
34	ExprTuple	38, 39
35	Variable
36	Variable
37	Variable
38	Variable
39	Operation	operator: 40 operand: 42
40	Literal
41	ExprTuple	42
42	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 ¶