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.logic import Equals
from proveit.numbers import Add, Neg, one
from proveit.physics.quantum.QPE import _s, _t

# build up the expression from sub-expressions
sub_expr1 = Neg(one)
sub_expr2 = Add(_t, sub_expr1, one)
sub_expr3 = Add(_s, sub_expr1, one)
expr = Equals(Add(sub_expr2, sub_expr3, sub_expr2, Add(Add(_t, _s), Neg(Add(_t, one)), one), sub_expr2, sub_expr3, sub_expr2, sub_expr3), Add(_t, _s, _t, _s, _t, _s, _t, _s)).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left(\left(t - 1 + 1\right) + \left(s - 1 + 1\right) + \left(t - 1 + 1\right) + \left(\left(t + s\right) - \left(t + 1\right) + 1\right) + \left(t - 1 + 1\right) + \left(s - 1 + 1\right) + \left(t - 1 + 1\right) + \left(s - 1 + 1\right)\right) =  \\ \left(t + s + t + s + t + s + t + s\right) \end{array} \end{array}

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.	()	(2)	('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	Operation	operator: 22 operands: 5
4	Operation	operator: 22 operands: 6
5	ExprTuple	8, 9, 8, 7, 8, 9, 8, 9
6	ExprTuple	24, 20, 24, 20, 24, 20, 24, 20
7	Operation	operator: 22 operands: 10
8	Operation	operator: 22 operands: 11
9	Operation	operator: 22 operands: 12
10	ExprTuple	13, 14, 25
11	ExprTuple	24, 15, 25
12	ExprTuple	20, 15, 25
13	Operation	operator: 22 operands: 16
14	Operation	operator: 18 operand: 21
15	Operation	operator: 18 operand: 25
16	ExprTuple	24, 20
17	ExprTuple	21
18	Literal
19	ExprTuple	25
20	Literal
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	24, 25
24	Literal
25	Literal