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, one, six
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, sub_expr2, one)
sub_expr4 = Add(_s, sub_expr2, one)
expr = Equals(Len(operands = [sub_expr3, Add(Add(_t, _s), Neg(Add(_t, one)), one), sub_expr3, sub_expr4, sub_expr3, sub_expr4]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, six)]))

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