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], instance_expr = Forall(instance_param_or_params = [B], instance_expr = Or(A, B), domain = Boolean, condition = Not(And(Not(A), Not(B)))), domain = 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 \in \mathbb{B}}~\left[\forall_{B \in \mathbb{B}~|~\lnot \left((\lnot A) \land (\lnot B)\right)}~\left(A \lor B\right)\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: 6 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 30 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 18 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	30, 21
9	Lambda	parameter: 31 body: 10
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 23 operands: 15
13	Literal
14	ExprTuple	30, 31
15	ExprTuple	16, 17
16	Operation	operator: 18 operands: 19
17	Operation	operator: 28 operand: 22
18	Literal
19	ExprTuple	31, 21
20	ExprTuple	22
21	Literal
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26
25	Operation	operator: 28 operand: 30
26	Operation	operator: 28 operand: 31
27	ExprTuple	30
28	Literal
29	ExprTuple	31
30	Variable
31	Variable