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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A, B], Equals(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(\left(A, B\right) \mapsto \left(\left(A \cong B\right) = \left[\forall_{x}~\left(\left(x \in A\right) = \left(x \in B\right)\right)\right]\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 7 body: 2
2	Operation	operator: 13 operands: 3
3	ExprTuple	4, 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