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
from proveit.linear_algebra import VecSpaces
from proveit.logic import And, InClass, InSet

# build up the expression from sub-expressions
sub_expr1 = VecSpaces(K)
expr = Conditional(And(InSet(A, U), InSet(B, V)), And(InClass(U, sub_expr1), InClass(V, sub_expr1)))

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())

\left\{\left(A \in U\right) \land \left(B \in V\right) \textrm{ if } U \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right) ,  V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 11 operands: 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 14 operands: 13
9	Operation	operator: 14 operands: 15
10	ExprTuple	16, 18
11	Literal
12	ExprTuple	17, 19
13	ExprTuple	18, 20
14	Literal
15	ExprTuple	19, 20
16	Variable
17	Variable
18	Variable
19	Variable
20	Operation	operator: 21 operand: 23
21	Literal
22	ExprTuple	23
23	Variable