Expression of type Conditional

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
from proveit.logic import Boolean, Forall, Implies, InSet, Not

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [B], instance_expr = A, conditions = [Implies(Not(A), B), Not(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\{\forall_{B~|~(\lnot A) \Rightarrow B, \lnot B}~A \textrm{ if } A \in \mathbb{B}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	22, 8
7	Lambda	parameter: 19 body: 9
8	Literal
9	Conditional	value: 22 condition: 10
10	Operation	operator: 11 operands: 12
11	Literal
12	ExprTuple	13, 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 20 operand: 19
15	Literal
16	ExprTuple	18, 19
17	ExprTuple	19
18	Operation	operator: 20 operand: 22
19	Variable
20	Literal
21	ExprTuple	22
22	Variable