Expression of type Forall

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, Forall, Functions, Image, InSet, Surjections

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f], instance_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())

\forall_{f}~\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()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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