Expression of type Equals

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, f
from proveit.logic import And, Equals, Functions, Image, InSet, Surjections

# build up the expression from sub-expressions
expr = 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())

\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}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

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