Expression of type Conditional

from the theory of proveit.logic.sets.subtraction

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, S, x, y
from proveit.logic import And, Difference, InSet, NotEquals, Set

# build up the expression from sub-expressions
expr = Conditional(And(InSet(x, S), NotEquals(x, y)), InSet(x, Difference(S, Set(y))))

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(x \in S\right) \land \left(x \neq y\right) \textrm{ if } x \in \left(S - \left\{y\right\}\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: 3 operands: 4
2	Operation	operator: 9 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	15, 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 13 operands: 14
9	Literal
10	ExprTuple	15, 16
11	Literal
12	ExprTuple	15, 20
13	Literal
14	ExprTuple	16, 17
15	Variable
16	Variable
17	Operation	operator: 18 operand: 20
18	Literal
19	ExprTuple	20
20	Variable