Expression of type Lambda

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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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