Expression of type ExprTuple

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, ExprTuple, Lambda, 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 = ExprTuple(Lambda([x, S], 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(\left(x, S\right) \mapsto \left\{|S \cup \left\{x\right\}| = \left(|S| + 1\right) \textrm{ if } |S| \in \mathbb{N} ,  x \notin S\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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