Expression of type ExprTuple

from the theory of proveit.logic.sets.equivalence

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, ExprTuple, x
from proveit.logic import Equals, Forall, InSet, SetEquiv

# build up the expression from sub-expressions
expr = ExprTuple(SetEquiv(A, B), Forall(instance_param_or_params = [x], instance_expr = Equals(InSet(x, A), InSet(x, B))))

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 \cong B, \forall_{x}~\left(\left(x \in A\right) = \left(x \in B\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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