Expression of type Implies

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 import Variable
from proveit.logic import Equals, Implies, 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)
expr = Implies(Variable("_a", latex_format = r"{_{-}a}"), Or(Equals(sub_expr1, zero), NotInSet(sub_expr1, Integer)))

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())

{_{-}a} \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)

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: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Variable
4	Operation	operator: 5 operands: 6
5	Literal
6	ExprTuple	7, 8
7	Operation	operator: 9 operands: 10
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	14, 13
11	Literal
12	ExprTuple	14, 15
13	Literal
14	Operation	operator: 16 operands: 17
15	Literal
16	Literal
17	ExprTuple	18, 19
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operand: 26
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26
24	Literal
25	Literal
26	Variable