Expression of type And

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 e, l
from proveit.logic import And, InSet, Union
from proveit.numbers import ModAbs, greater
from proveit.physics.quantum.QPE import _neg_domain, _pos_domain, _two_pow_t

# build up the expression from sub-expressions
expr = And(InSet(l, Union(_neg_domain, _pos_domain)), greater(ModAbs(l, _two_pow_t), e))

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(l \in \left(\{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\} \cup \{e + 1~\ldotp \ldotp~2^{t - 1}\}\right)\right) \land \left(\left|l\right|_{\textup{mod}\thinspace 2^{t}} > e\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',)

# 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: 7 operands: 8
5	Literal
6	ExprTuple	17, 9
7	Literal
8	ExprTuple	32, 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18
15	Operation	operator: 20 operands: 19
16	Operation	operator: 20 operands: 21
17	Variable
18	Operation	operator: 33 operands: 22
19	ExprTuple	23, 24
20	Literal
21	ExprTuple	28, 31
22	ExprTuple	35, 39
23	Operation	operator: 37 operands: 25
24	Operation	operator: 41 operand: 28
25	ExprTuple	27, 43
26	ExprTuple	28
27	Operation	operator: 41 operand: 31
28	Operation	operator: 37 operands: 30
29	ExprTuple	31
30	ExprTuple	32, 43
31	Operation	operator: 33 operands: 34
32	Variable
33	Literal
34	ExprTuple	35, 36
35	Literal
36	Operation	operator: 37 operands: 38
37	Literal
38	ExprTuple	39, 40
39	Literal
40	Operation	operator: 41 operand: 43
41	Literal
42	ExprTuple	43
43	Literal