Expression of type Forall

from the theory of proveit.logic.booleans.disjunction

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 And, Boolean, Forall, Not, Or

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A, B], instance_expr = Or(A, B), domain = Boolean, condition = Not(And(Not(A), Not(B))))

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 \in \mathbb{B}~|~\lnot \left((\lnot A) \land (\lnot B)\right)}~\left(A \lor B\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: 8 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 19 operands: 9
7	Literal
8	ExprTuple	26, 27
9	ExprTuple	10, 11, 12
10	Operation	operator: 14 operands: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 24 operand: 18
13	ExprTuple	26, 17
14	Literal
15	ExprTuple	27, 17
16	ExprTuple	18
17	Literal
18	Operation	operator: 19 operands: 20
19	Literal
20	ExprTuple	21, 22
21	Operation	operator: 24 operand: 26
22	Operation	operator: 24 operand: 27
23	ExprTuple	26
24	Literal
25	ExprTuple	27
26	Variable
27	Variable