Expression of type Lambda

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, B, Conditional, Lambda, f
from proveit.logic import And, Bijections, InSet, Injections, Surjections

# build up the expression from sub-expressions
expr = Lambda(f, Conditional(And(InSet(f, Injections(A, B)), InSet(f, Surjections(A, B))), InSet(f, Bijections(A, B))))

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())

f \mapsto \left\{\left(f \in \left[A \xrightarrow[]{\text{1-to-1}} B\right]\right) \land \left(f \in \left[A \xrightarrow[\text{onto}]{} B\right]\right) \textrm{ if } f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\right]\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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