Expression of type ExprTuple

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 ExprTuple, e, l
from proveit.logic import And, InSet
from proveit.numbers import Less, ModAbs, greater, zero
from proveit.physics.quantum.QPE import _e_domain, _full_domain, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(InSet(e, _e_domain), And(InSet(l, _full_domain), greater(ModAbs(l, _two_pow_t), e)), Less(l, zero))

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(e \in \{1~\ldotp \ldotp~2^{t - 1} - 2\}, \left(l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\}\right) \land \left(\left|l\right|_{\textup{mod}\thinspace 2^{t}} > e\right), l < 0\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2, 3
1	Operation	operator: 13 operands: 4
2	Operation	operator: 5 operands: 6
3	Operation	operator: 15 operands: 7
4	ExprTuple	19, 8
5	Literal
6	ExprTuple	9, 10
7	ExprTuple	28, 11
8	Operation	operator: 22 operands: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operands: 16
11	Literal
12	ExprTuple	46, 17
13	Literal
14	ExprTuple	28, 18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 40 operands: 21
18	Operation	operator: 22 operands: 23
19	Variable
20	Operation	operator: 24 operands: 25
21	ExprTuple	35, 26
22	Literal
23	ExprTuple	27, 35
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 44 operand: 38
27	Operation	operator: 40 operands: 31
28	Variable
29	Operation	operator: 36 operands: 32
30	ExprTuple	38
31	ExprTuple	33, 46
32	ExprTuple	38, 42
33	Operation	operator: 44 operand: 35
34	ExprTuple	35
35	Operation	operator: 36 operands: 37
36	Literal
37	ExprTuple	38, 39
38	Literal
39	Operation	operator: 40 operands: 41
40	Literal
41	ExprTuple	42, 43
42	Literal
43	Operation	operator: 44 operand: 46
44	Literal
45	ExprTuple	46
46	Literal