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, Forall, InSet, Injections, Surjections

# build up the expression from sub-expressions
expr = Lambda([A, B], Forall(instance_param_or_params = [f], instance_expr = 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())

\left(A, B\right) \mapsto \left[\forall_{f}~\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)\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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