Expression of type Equals

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, C, Conditional
from proveit.logic import And, Boolean, Equals, Implies, InSet, Not

# build up the expression from sub-expressions
sub_expr1 = InSet(A, Boolean)
sub_expr2 = Implies(A, C)
sub_expr3 = Implies(Not(A), C)
expr = Equals(Conditional(C, And(sub_expr1, And(sub_expr2, sub_expr3))), Conditional(C, And(sub_expr1, sub_expr2, sub_expr3))).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\{C \textrm{ if } A \in \mathbb{B} ,  \left(A \Rightarrow C\right) \land \left((\lnot A) \Rightarrow C\right)\right.. \\  = \left\{C \textrm{ if } A \in \mathbb{B} ,  A \Rightarrow C ,  (\lnot A) \Rightarrow C\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: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Conditional	value: 22 condition: 5
4	Conditional	value: 22 condition: 6
5	Operation	operator: 11 operands: 7
6	Operation	operator: 11 operands: 8
7	ExprTuple	10, 9
8	ExprTuple	10, 15, 16
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	25, 17
15	Operation	operator: 19 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	25, 22
19	Literal
20	ExprTuple	21, 22
21	Operation	operator: 23 operand: 25
22	Variable
23	Literal
24	ExprTuple	25
25	Variable