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, Equals, Forall, Implies

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A], instance_expr = Forall(instance_param_or_params = [B], instance_expr = Equals(A, B), domain = Boolean, conditions = [Implies(A, B), Implies(B, A)]), 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}~|~A \Rightarrow B, B \Rightarrow A}~\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: 28 body: 4
3	ExprTuple	28
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 21 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	28, 26
10	Lambda	parameter: 27 body: 12
11	ExprTuple	27
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 23
14	Operation	operator: 16 operands: 17
15	Literal
16	Literal
17	ExprTuple	18, 19, 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 24 operands: 23
20	Operation	operator: 24 operands: 25
21	Literal
22	ExprTuple	27, 26
23	ExprTuple	28, 27
24	Literal
25	ExprTuple	27, 28
26	Literal
27	Variable
28	Variable