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

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

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