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, subtract, two, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [ExprRange(sub_expr1, Equals(Add(sub_expr1, t), Add(Add(sub_expr1, Neg(one), t), one)), Add(Neg(t), two), zero)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, subtract(t, 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(1, 2, \ldots, \left(t - 1\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: 18 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7
5	Literal
6	ExprTuple	8
7	ExprRange	lambda_map: 9 start_index: 10 end_index: 11
8	ExprRange	lambda_map: 12 start_index: 35 end_index: 13
9	Lambda	parameter: 30 body: 14
10	Operation	operator: 28 operands: 15
11	Literal
12	Lambda	parameter: 30 body: 30
13	Operation	operator: 28 operands: 17
14	Operation	operator: 18 operands: 19
15	ExprTuple	20, 21
16	ExprTuple	30
17	ExprTuple	32, 31
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 33 operand: 32
21	Literal
22	Operation	operator: 28 operands: 25
23	Operation	operator: 28 operands: 26
24	ExprTuple	32
25	ExprTuple	30, 32
26	ExprTuple	27, 35
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31, 32
30	Variable
31	Operation	operator: 33 operand: 35
32	Variable
33	Literal
34	ExprTuple	35
35	Literal