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, Mult, Neg, one, three
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(Add(_t, _s), Neg(Add(_t, one)), one)
expr = Equals(Add(sub_expr2, Add(_s, sub_expr1, one), sub_expr2, sub_expr3, sub_expr2, sub_expr3), Add(Mult(three, _t), Mult(three, _s)))

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