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, t
from proveit.core_expr_types import Len
from proveit.logic import And, Equals
from proveit.numbers import Add, Neg, four, one, two, zero
from proveit.physics.quantum.QPE import _s

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(t, _s)
expr = Equals(Len(operands = [Equals(zero, zero), Equals(one, Add(zero, one)), And(ExprRange(sub_expr1, Equals(Add(sub_expr1, t), Add(Add(sub_expr1, Neg(one), t), one)), Add(Neg(t), two), zero)), Equals(sub_expr2, sub_expr2)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, four)]))

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(0 = 0, 1 = \left(0 + 1\right), \left(\left(\left(-t + 2\right) + t\right) = \left(\left(\left(-t + 2\right) - 1 + t\right) + 1\right)\right) \land  \left(\left(\left(-t + 3\right) + t\right) = \left(\left(\left(-t + 3\right) - 1 + t\right) + 1\right)\right) \land  \ldots \land  \left(\left(0 + t\right) = \left(\left(0 - 1 + t\right) + 1\right)\right), \left(t + s\right) = \left(t + s\right)\right)| = |\left(1, 2, \ldots, 4\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: 31 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8, 9, 10
5	Literal
6	ExprTuple	11
7	Operation	operator: 31 operands: 12
8	Operation	operator: 31 operands: 13
9	Operation	operator: 14 operands: 15
10	Operation	operator: 31 operands: 16
11	ExprRange	lambda_map: 17 start_index: 48 end_index: 18
12	ExprTuple	26, 26
13	ExprTuple	48, 19
14	Literal
15	ExprTuple	20
16	ExprTuple	21, 21
17	Lambda	parameter: 43 body: 43
18	Literal
19	Operation	operator: 41 operands: 22
20	ExprRange	lambda_map: 23 start_index: 24 end_index: 26
21	Operation	operator: 41 operands: 25
22	ExprTuple	26, 48
23	Lambda	parameter: 43 body: 28
24	Operation	operator: 41 operands: 29
25	ExprTuple	45, 30
26	Literal
27	ExprTuple	43
28	Operation	operator: 31 operands: 32
29	ExprTuple	33, 34
30	Literal
31	Literal
32	ExprTuple	35, 36
33	Operation	operator: 46 operand: 45
34	Literal
35	Operation	operator: 41 operands: 38
36	Operation	operator: 41 operands: 39
37	ExprTuple	45
38	ExprTuple	43, 45
39	ExprTuple	40, 48
40	Operation	operator: 41 operands: 42
41	Literal
42	ExprTuple	43, 44, 45
43	Variable
44	Operation	operator: 46 operand: 48
45	Variable
46	Literal
47	ExprTuple	48
48	Literal