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.logic import Equals
from proveit.numbers import Add, Neg, 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 = Neg(t)
sub_expr3 = Add(t, _s)
expr = Equals([zero, ExprRange(sub_expr1, Add(sub_expr1, Neg(one), t), Add(sub_expr2, two), zero), t, sub_expr3], [zero, ExprRange(sub_expr1, Add(sub_expr1, t), Add(sub_expr2, one), zero), sub_expr3])

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,\left(\left(-t + 2\right) - 1 + t\right), \left(\left(-t + 3\right) - 1 + t\right), \ldots, \left(0 - 1 + t\right), t, t + s\right) = \left(0,\left(\left(-t + 1\right) + t\right), \left(\left(-t + 2\right) + t\right), \ldots, \left(0 + t\right), t + s\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	ExprTuple	12, 5, 30, 7
4	ExprTuple	12, 6, 7
5	ExprRange	lambda_map: 8 start_index: 9 end_index: 12
6	ExprRange	lambda_map: 10 start_index: 11 end_index: 12
7	Operation	operator: 22 operands: 13
8	Lambda	parameter: 26 body: 14
9	Operation	operator: 22 operands: 15
10	Lambda	parameter: 26 body: 17
11	Operation	operator: 22 operands: 18
12	Literal
13	ExprTuple	30, 19
14	Operation	operator: 22 operands: 20
15	ExprTuple	24, 21
16	ExprTuple	26
17	Operation	operator: 22 operands: 23
18	ExprTuple	24, 31
19	Literal
20	ExprTuple	26, 25, 30
21	Literal
22	Literal
23	ExprTuple	26, 30
24	Operation	operator: 28 operand: 30
25	Operation	operator: 28 operand: 31
26	Variable
27	ExprTuple	30
28	Literal
29	ExprTuple	31
30	Variable
31	Literal