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 ModAbs, greater, greater_eq, 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)), greater_eq(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 \geq 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: 14 operands: 4
2	Operation	operator: 5 operands: 6
3	Operation	operator: 7 operands: 8
4	ExprTuple	20, 9
5	Literal
6	ExprTuple	10, 11
7	Literal
8	ExprTuple	12, 29
9	Operation	operator: 23 operands: 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 16 operands: 17
12	Literal
13	ExprTuple	47, 18
14	Literal
15	ExprTuple	29, 19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 41 operands: 22
19	Operation	operator: 23 operands: 24
20	Variable
21	Operation	operator: 25 operands: 26
22	ExprTuple	36, 27
23	Literal
24	ExprTuple	28, 36
25	Literal
26	ExprTuple	29, 30
27	Operation	operator: 45 operand: 39
28	Operation	operator: 41 operands: 32
29	Variable
30	Operation	operator: 37 operands: 33
31	ExprTuple	39
32	ExprTuple	34, 47
33	ExprTuple	39, 43
34	Operation	operator: 45 operand: 36
35	ExprTuple	36
36	Operation	operator: 37 operands: 38
37	Literal
38	ExprTuple	39, 40
39	Literal
40	Operation	operator: 41 operands: 42
41	Literal
42	ExprTuple	43, 44
43	Literal
44	Operation	operator: 45 operand: 47
45	Literal
46	ExprTuple	47
47	Literal