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 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 = Add(Neg(t), two)
expr = Equals(Len(operands = [ExprRange(sub_expr1, Equals(Add(sub_expr1, t), Add(Add(sub_expr1, Neg(one), t), one)), sub_expr2, zero)]), Add(zero, Neg(sub_expr2), 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(\left(-t + 2\right) + t\right) = \left(\left(\left(-t + 2\right) - 1 + t\right) + 1\right)\right), \left(\left(\left(-t + 3\right) + t\right) = \left(\left(\left(-t + 3\right) - 1 + t\right) + 1\right)\right), \ldots, \left(\left(0 + t\right) = \left(\left(0 - 1 + t\right) + 1\right)\right)\right)| = \left(0 - \left(-t + 2\right) + 1\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: 15 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 26 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	10, 8, 33
7	ExprRange	lambda_map: 9 start_index: 14 end_index: 10
8	Operation	operator: 31 operand: 14
9	Lambda	parameter: 28 body: 13
10	Literal
11	ExprTuple	14
12	ExprTuple	28
13	Operation	operator: 15 operands: 16
14	Operation	operator: 26 operands: 17
15	Literal
16	ExprTuple	18, 19
17	ExprTuple	20, 21
18	Operation	operator: 26 operands: 22
19	Operation	operator: 26 operands: 23
20	Operation	operator: 31 operand: 30
21	Literal
22	ExprTuple	28, 30
23	ExprTuple	25, 33
24	ExprTuple	30
25	Operation	operator: 26 operands: 27
26	Literal
27	ExprTuple	28, 29, 30
28	Variable
29	Operation	operator: 31 operand: 33
30	Variable
31	Literal
32	ExprTuple	33
33	Literal