Expression of type Forall

from the theory of proveit.logic.booleans

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, Function, P
from proveit.logic import Boolean, Forall

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A], instance_expr = Forall(instance_param_or_params = [B], instance_expr = Function(P, [A, B]), domain = Boolean), 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}}~P\left(A, 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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 19 body: 4
3	ExprTuple	19
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 17 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	19, 21
10	Lambda	parameter: 20 body: 12
11	ExprTuple	20
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Variable
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	20, 21
19	Variable
20	Variable
21	Literal