Expression of type Implies

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
sub_expr1 = Equals(A, B)
sub_expr2 = [Implies(A, B), Implies(B, A)]
expr = Implies(Forall(instance_param_or_params = [A], instance_expr = Forall(instance_param_or_params = [B], instance_expr = sub_expr1, domain = Boolean, conditions = sub_expr2), domain = Boolean), Forall(instance_param_or_params = [A, B], instance_expr = sub_expr1, domain = Boolean, conditions = sub_expr2)).with_wrapping_at(1)

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())

\begin{array}{c} \begin{array}{l} \left[\forall_{A \in \mathbb{B}}~\left[\forall_{B \in \mathbb{B}~|~A \Rightarrow B, B \Rightarrow A}~\left(A = B\right)\right]\right] \\  \Rightarrow \left[\forall_{A, B \in \mathbb{B}~|~A \Rightarrow B, B \Rightarrow A}~\left(A = B\right)\right] \end{array} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(1)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 32 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 13 operand: 6
3	Operation	operator: 13 operand: 7
4	ExprTuple	6
5	ExprTuple	7
6	Lambda	parameter: 36 body: 9
7	Lambda	parameters: 31 body: 10
8	ExprTuple	36
9	Conditional	value: 11 condition: 17
10	Conditional	value: 21 condition: 12
11	Operation	operator: 13 operand: 16
12	Operation	operator: 24 operands: 15
13	Literal
14	ExprTuple	16
15	ExprTuple	17, 26, 27, 28
16	Lambda	parameter: 35 body: 19
17	Operation	operator: 29 operands: 20
18	ExprTuple	35
19	Conditional	value: 21 condition: 22
20	ExprTuple	36, 34
21	Operation	operator: 23 operands: 31
22	Operation	operator: 24 operands: 25
23	Literal
24	Literal
25	ExprTuple	26, 27, 28
26	Operation	operator: 29 operands: 30
27	Operation	operator: 32 operands: 31
28	Operation	operator: 32 operands: 33
29	Literal
30	ExprTuple	35, 34
31	ExprTuple	36, 35
32	Literal
33	ExprTuple	35, 36
34	Literal
35	Variable
36	Variable