Expression of type Equals

from the theory of proveit.physics.quantum.QPE

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.logic import Equals, Implies, Not, NotEquals, NotInSet, Or
from proveit.numbers import Integer, Mult, zero
from proveit.physics.quantum.QPE import _delta_b, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Mult(_two_pow_t, _delta_b)
sub_expr2 = Equals(sub_expr1, zero)
sub_expr3 = Or(sub_expr2, NotInSet(sub_expr1, Integer))
expr = Equals(Implies(NotEquals(sub_expr1, zero), sub_expr3), Implies(Not(sub_expr2), sub_expr3))

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())

\left(\left(\left(2^{t} \cdot \delta_{b}\right) \neq 0\right) \Rightarrow \left(\left(\left(2^{t} \cdot \delta_{b}\right) = 0\right) \lor \left(\left(2^{t} \cdot \delta_{b}\right) \notin \mathbb{Z}\right)\right)\right) = \left((\lnot \left(\left(2^{t} \cdot \delta_{b}\right) = 0\right)) \Rightarrow \left(\left(\left(2^{t} \cdot \delta_{b}\right) = 0\right) \lor \left(\left(2^{t} \cdot \delta_{b}\right) \notin \mathbb{Z}\right)\right)\right)

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.	()	()	('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: 17 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 9
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 10 operands: 18
8	Operation	operator: 11 operand: 15
9	Operation	operator: 13 operands: 14
10	Literal
11	Literal
12	ExprTuple	15
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	22, 21
19	Literal
20	ExprTuple	22, 23
21	Literal
22	Operation	operator: 24 operands: 25
23	Literal
24	Literal
25	ExprTuple	26, 27
26	Operation	operator: 28 operands: 29
27	Operation	operator: 30 operand: 34
28	Literal
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	34
32	Literal
33	Literal
34	Variable