Expression of type Conditional

from the theory of proveit.logic.sets.functions.bijections

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, Conditional, f, n
from proveit.logic import And, Bijections, Card, Equals, Forall, Image, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
sub_expr1 = Image(f, A)
sub_expr2 = Card(A)
expr = Conditional(Forall(instance_param_or_params = [f, A], instance_expr = InSet(f, Bijections(A, sub_expr1)), condition = And(Equals(Card(sub_expr1), sub_expr2), Equals(sub_expr2, n)).with_total_ordering_style()), InSet(n, Natural))

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\{\forall_{f, A~|~|f^{\rightarrow}(A)| = |A|, |A| = n}~\left(f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} f^{\rightarrow}(A)\right]\right) \textrm{ if } n \in \mathbb{N}\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 operand: 6
2	Operation	operator: 11 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	25, 7
6	Lambda	parameters: 31 body: 8
7	Literal
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	32, 15
13	Literal
14	ExprTuple	16, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 21 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	ExprTuple	33, 29
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	24, 25
23	Operation	operator: 27 operand: 29
24	Operation	operator: 27 operand: 33
25	Variable
26	ExprTuple	29
27	Literal
28	ExprTuple	33
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Variable
33	Variable