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

# build up the expression from sub-expressions
expr = Lambda(f, Equals(InSet(f, Bijections(A, B)), And(InSet(f, Injections(A, B)), InSet(f, Surjections(A, B)))).with_wrapping_at(2))

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(\begin{array}{c} \begin{array}{l} \left(f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\right]\right) =  \\ \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)\right) \end{array} \end{array}\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 18 body: 2
1	ExprTuple	18
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 15 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	18, 10
8	Literal
9	ExprTuple	11, 12
10	Operation	operator: 13 operands: 22
11	Operation	operator: 15 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	18, 17
15	Literal
16	ExprTuple	18, 19
17	Operation	operator: 20 operands: 22
18	Variable
19	Operation	operator: 21 operands: 22
20	Literal
21	Literal
22	ExprTuple	23, 24
23	Variable
24	Variable