Expression of type Lambda

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

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, Equals, Functions, Image, InSet, Surjections

# build up the expression from sub-expressions
expr = Lambda(f, Equals(InSet(f, Surjections(A, B)), And(InSet(f, Functions(A, B)), Equals(Image(f, 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}]{} B\right]\right) =  \\ \left(\left(f \in \left[A \rightarrow B\right]\right) \land \left(f^{\rightarrow}(A) = B\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: 24 body: 2
1	ExprTuple	24
2	Operation	operator: 15 operands: 3
3	ExprTuple	4, 5
4	Operation	operator: 13 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	24, 9
7	Literal
8	ExprTuple	10, 11
9	Operation	operator: 12 operands: 20
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operands: 16
12	Literal
13	Literal
14	ExprTuple	24, 17
15	Literal
16	ExprTuple	18, 23
17	Operation	operator: 19 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	25, 23
21	Literal
22	ExprTuple	24, 25
23	Variable
24	Variable
25	Variable