Expression of type SubsetEq

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 SubsetEq, Union
from proveit.physics.quantum.QPE import _full_domain, _neg_domain, _pos_domain

# build up the expression from sub-expressions
expr = SubsetEq(Union(_neg_domain, _pos_domain), _full_domain)

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(\{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\} \cup \{e + 1~\ldotp \ldotp~2^{t - 1}\}\right) \subseteq \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\}

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: 5 operands: 6
4	Operation	operator: 11 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	13, 21
8	Operation	operator: 11 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	18, 21
13	Operation	operator: 27 operands: 15
14	Operation	operator: 31 operand: 18
15	ExprTuple	17, 33
16	ExprTuple	18
17	Operation	operator: 31 operand: 21
18	Operation	operator: 27 operands: 20
19	ExprTuple	21
20	ExprTuple	22, 33
21	Operation	operator: 23 operands: 24
22	Variable
23	Literal
24	ExprTuple	25, 26
25	Literal
26	Operation	operator: 27 operands: 28
27	Literal
28	ExprTuple	29, 30
29	Literal
30	Operation	operator: 31 operand: 33
31	Literal
32	ExprTuple	33
33	Literal