Expression of type Forall

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

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A, B], instance_expr = Implies(Not(B), Not(A)), conditions = [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())

\forall_{A, B~|~A \Rightarrow B, A \in \mathbb{B}}~\left((\lnot B) \Rightarrow (\lnot A)\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 18 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 17 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 15 operand: 21
11	Operation	operator: 15 operand: 22
12	Operation	operator: 17 operands: 18
13	Operation	operator: 19 operands: 20
14	ExprTuple	21
15	Literal
16	ExprTuple	22
17	Literal
18	ExprTuple	22, 21
19	Literal
20	ExprTuple	22, 23
21	Variable
22	Variable
23	Literal