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, Implies, InSet, Not

# build up the expression from sub-expressions
expr = Lambda([A, B], Conditional(Implies(Not(B), Not(A)), And(Implies(A, B), InSet(A, Boolean))))

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\{(\lnot B) \Rightarrow (\lnot A) \textrm{ if } A \Rightarrow B ,  A \in \mathbb{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: 15 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 14 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 12 operand: 18
8	Operation	operator: 12 operand: 19
9	Operation	operator: 14 operands: 15
10	Operation	operator: 16 operands: 17
11	ExprTuple	18
12	Literal
13	ExprTuple	19
14	Literal
15	ExprTuple	19, 18
16	Literal
17	ExprTuple	19, 20
18	Variable
19	Variable
20	Literal