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 ExprRange, ExprTuple, Variable, e
from proveit.core_expr_types import Len
from proveit.numbers import Add, LessEq, Neg, one, three
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(e, one)
expr = ExprTuple(Len(operands = [LessEq(Add(Neg(_two_pow__t_minus_one), one), sub_expr2), LessEq(sub_expr2, _two_pow__t_minus_one), LessEq(_two_pow__t_minus_one, _two_pow__t_minus_one)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, three)]))

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(\left(-2^{t - 1} + 1\right) \leq \left(e + 1\right), \left(e + 1\right) \leq 2^{t - 1}, 2^{t - 1} \leq 2^{t - 1}\right)|, |\left(1, 2, \ldots, 3\right)|\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
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7, 8
4	Literal
5	ExprTuple	9
6	Operation	operator: 12 operands: 10
7	Operation	operator: 12 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprRange	lambda_map: 14 start_index: 36 end_index: 15
10	ExprTuple	16, 17
11	ExprTuple	17, 25
12	Literal
13	ExprTuple	25, 25
14	Lambda	parameter: 21 body: 21
15	Literal
16	Operation	operator: 30 operands: 19
17	Operation	operator: 30 operands: 20
18	ExprTuple	21
19	ExprTuple	22, 36
20	ExprTuple	23, 36
21	Variable
22	Operation	operator: 34 operand: 25
23	Variable
24	ExprTuple	25
25	Operation	operator: 26 operands: 27
26	Literal
27	ExprTuple	28, 29
28	Literal
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Operation	operator: 34 operand: 36
34	Literal
35	ExprTuple	36
36	Literal