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

# build up the expression from sub-expressions
expr = Lambda([A, B], Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(InSet(x, A), InSet(x, B))), SetEquiv(A, 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\{\forall_{x}~\left(\left(x \in A\right) = \left(x \in B\right)\right) \textrm{ if } A \cong B\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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