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 import ExprRange, Variable, e
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Add, Less, LessEq, Neg, one, three
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(e, one)
sub_expr3 = Neg(sub_expr2)
expr = Equals(Len(operands = [LessEq(Add(Neg(_two_pow__t_minus_one), one), sub_expr3), Less(sub_expr3, sub_expr2), LessEq(sub_expr2, _two_pow__t_minus_one)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, three)]))

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(-2^{t - 1} + 1\right) \leq \left(-\left(e + 1\right)\right), \left(-\left(e + 1\right)\right) < \left(e + 1\right), \left(e + 1\right) \leq 2^{t - 1}\right)| = |\left(1, 2, \ldots, 3\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	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9, 10
6	Literal
7	ExprTuple	11
8	Operation	operator: 15 operands: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operands: 16
11	ExprRange	lambda_map: 17 start_index: 41 end_index: 18
12	ExprTuple	19, 20
13	Literal
14	ExprTuple	20, 26
15	Literal
16	ExprTuple	26, 29
17	Lambda	parameter: 24 body: 24
18	Literal
19	Operation	operator: 35 operands: 22
20	Operation	operator: 39 operand: 26
21	ExprTuple	24
22	ExprTuple	25, 41
23	ExprTuple	26
24	Variable
25	Operation	operator: 39 operand: 29
26	Operation	operator: 35 operands: 28
27	ExprTuple	29
28	ExprTuple	30, 41
29	Operation	operator: 31 operands: 32
30	Variable
31	Literal
32	ExprTuple	33, 34
33	Literal
34	Operation	operator: 35 operands: 36
35	Literal
36	ExprTuple	37, 38
37	Literal
38	Operation	operator: 39 operand: 41
39	Literal
40	ExprTuple	41
41	Literal