Theorem set_equiv_fold of type Forall

from the theory of proveit.logic.sets.equivalence

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.logic.sets.equivalence import set_equiv_fold

# check that the built expression is the same as the stored expression
assert set_equiv_fold.expr == stored_expr
assert set_equiv_fold.expr._style_id == stored_expr._style_id
print("Passed sanity check: set_equiv_fold matches stored_expr")

Passed sanity check: set_equiv_fold matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{A, B~|~\forall_{x}~\left(\left(x \in A\right) = \left(x \in B\right)\right)}~\left(A \cong B\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: 8 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 7 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operand: 10
6	Literal
7	ExprTuple	20, 22
8	Literal
9	ExprTuple	10
10	Lambda	parameter: 21 body: 12
11	ExprTuple	21
12	Operation	operator: 13 operands: 14
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 18 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	21, 20
18	Literal
19	ExprTuple	21, 22
20	Variable
21	Variable
22	Variable