Expression of type Lambda

from the theory of proveit.logic.booleans.implication

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
from proveit.logic import And, Boolean, Equals, Implies, InSet

# build up the expression from sub-expressions
expr = Lambda([A, B], Conditional(Equals(A, B), And(InSet(A, Boolean), InSet(B, Boolean), Implies(A, B), Implies(B, A))))

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\{A = B \textrm{ if } A \in \mathbb{B} ,  B \in \mathbb{B} ,  A \Rightarrow B ,  B \Rightarrow A\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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