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, 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 = Neg(Add(e, one))
sub_expr3 = Add(Neg(_two_pow__t_minus_one), one)
expr = Equals(Len(operands = [LessEq(sub_expr3, sub_expr3), LessEq(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(-2^{t - 1} + 1\right), \left(-2^{t - 1} + 1\right) \leq \left(-\left(e + 1\right)\right), \left(-\left(e + 1\right)\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: 14 operands: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprRange	lambda_map: 16 start_index: 40 end_index: 17
12	ExprTuple	18, 18
13	ExprTuple	18, 19
14	Literal
15	ExprTuple	19, 28
16	Lambda	parameter: 23 body: 23
17	Literal
18	Operation	operator: 34 operands: 21
19	Operation	operator: 38 operand: 25
20	ExprTuple	23
21	ExprTuple	24, 40
22	ExprTuple	25
23	Variable
24	Operation	operator: 38 operand: 28
25	Operation	operator: 34 operands: 27
26	ExprTuple	28
27	ExprTuple	29, 40
28	Operation	operator: 30 operands: 31
29	Variable
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37
36	Literal
37	Operation	operator: 38 operand: 40
38	Literal
39	ExprTuple	40
40	Literal