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 Boolean, Forall, Implies, InSet, Not

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

A \mapsto \left\{\forall_{B~|~(\lnot A) \Rightarrow B, \lnot B}~A \textrm{ if } 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	parameter: 23 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	23, 9
8	Lambda	parameter: 20 body: 10
9	Literal
10	Conditional	value: 23 condition: 11
11	Operation	operator: 12 operands: 13
12	Literal
13	ExprTuple	14, 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 21 operand: 20
16	Literal
17	ExprTuple	19, 20
18	ExprTuple	20
19	Operation	operator: 21 operand: 23
20	Variable
21	Literal
22	ExprTuple	23
23	Variable