Expression of type Lambda

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

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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