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
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Add, Neg, five, one
from proveit.physics.quantum.QPE import _s, _t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Neg(one)
sub_expr3 = Add(_t, _s)
sub_expr4 = Add(_t, sub_expr2, one)
expr = Equals(Len(operands = [sub_expr4, Add(_s, sub_expr2, one), sub_expr4, Add(sub_expr3, Neg(Add(_t, one)), one), Add(sub_expr3, sub_expr2, one)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, five)]))

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(t - 1 + 1, s - 1 + 1, t - 1 + 1, \left(t + s\right) - \left(t + 1\right) + 1, \left(t + s\right) - 1 + 1\right)| = |\left(1, 2, \ldots, 5\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	9, 8, 9, 10, 11
6	Literal
7	ExprTuple	12
8	Operation	operator: 30 operands: 13
9	Operation	operator: 30 operands: 14
10	Operation	operator: 30 operands: 15
11	Operation	operator: 30 operands: 16
12	ExprRange	lambda_map: 17 start_index: 33 end_index: 18
13	ExprTuple	29, 21, 33
14	ExprTuple	32, 21, 33
15	ExprTuple	20, 19, 33
16	ExprTuple	20, 21, 33
17	Lambda	parameter: 27 body: 27
18	Literal
19	Operation	operator: 25 operand: 28
20	Operation	operator: 30 operands: 24
21	Operation	operator: 25 operand: 33
22	ExprTuple	27
23	ExprTuple	28
24	ExprTuple	32, 29
25	Literal
26	ExprTuple	33
27	Variable
28	Operation	operator: 30 operands: 31
29	Literal
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Literal