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 Conditional, ExprTuple, Lambda, m
from proveit.logic import And, InSet
from proveit.numbers import Exp, LessEq, ModAbs, one, subtract, two
from proveit.physics.quantum.QPE import _b_floor, _m_domain, _n, _success_cond, _t, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(_success_cond, And(InSet(m, _m_domain), LessEq(ModAbs(subtract(m, _b_floor), _two_pow_t), subtract(Exp(two, subtract(_t, _n)), one))))))

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(m \mapsto \left\{\left|\frac{m}{2^{t}} - \varphi\right|_{\textup{mod}\thinspace 1} \leq 2^{-n} \textrm{ if } m \in \{0~\ldotp \ldotp~2^{t} - 1\} ,  \left|m - b_{\textit{f}}\right|_{\textup{mod}\thinspace 2^{t}} \leq \left(2^{t - n} - 1\right)\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 44 body: 3
2	ExprTuple	44
3	Conditional	value: 4 condition: 5
4	Operation	operator: 17 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 26 operands: 13
10	Operation	operator: 47 operands: 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 17 operands: 18
13	ExprTuple	19, 54
14	ExprTuple	53, 57
15	Literal
16	ExprTuple	44, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 51 operands: 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Operation	operator: 51 operands: 28
23	ExprTuple	29, 30
24	Literal
25	ExprTuple	31, 32
26	Literal
27	ExprTuple	33, 42
28	ExprTuple	34, 43
29	Operation	operator: 35 operands: 36
30	Operation	operator: 58 operand: 41
31	Literal
32	Operation	operator: 51 operands: 38
33	Operation	operator: 51 operands: 39
34	Operation	operator: 47 operands: 40
35	Literal
36	ExprTuple	44, 42
37	ExprTuple	41
38	ExprTuple	42, 43
39	ExprTuple	44, 45
40	ExprTuple	53, 46
41	Literal
42	Operation	operator: 47 operands: 48
43	Operation	operator: 58 operand: 54
44	Variable
45	Operation	operator: 58 operand: 55
46	Operation	operator: 51 operands: 52
47	Literal
48	ExprTuple	53, 56
49	ExprTuple	54
50	ExprTuple	55
51	Literal
52	ExprTuple	56, 57
53	Literal
54	Literal
55	Literal
56	Literal
57	Operation	operator: 58 operand: 60
58	Literal
59	ExprTuple	60
60	Literal