Expression of type Conditional

from the theory of proveit.logic.sets.cardinality

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
from proveit.logic import And, Card, Equals, InSet, NotInSet, Set, Union
from proveit.numbers import Add, Natural, one

# build up the expression from sub-expressions
sub_expr1 = Card(S)
expr = Conditional(Equals(Card(Union(S, Set(x))), Add(sub_expr1, one)), And(InSet(sub_expr1, Natural), NotInSet(x, S)))

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\{|S \cup \left\{x\right\}| = \left(|S| + 1\right) \textrm{ if } |S| \in \mathbb{N} ,  x \notin S\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: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 24 operand: 18
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operands: 15
10	Operation	operator: 16 operands: 17
11	ExprTuple	18
12	Literal
13	ExprTuple	20, 19
14	Literal
15	ExprTuple	20, 21
16	Literal
17	ExprTuple	30, 27
18	Operation	operator: 22 operands: 23
19	Literal
20	Operation	operator: 24 operand: 27
21	Literal
22	Literal
23	ExprTuple	27, 26
24	Literal
25	ExprTuple	27
26	Operation	operator: 28 operand: 30
27	Variable
28	Literal
29	ExprTuple	30
30	Variable