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, e, l
from proveit.logic import And, Iff, InSet, Union
from proveit.numbers import ModAbs, greater
from proveit.physics.quantum.QPE import _e_domain, _full_domain, _neg_domain, _pos_domain, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = greater(ModAbs(l, _two_pow_t), e)
expr = Lambda(e, Conditional(Iff(And(InSet(l, Union(_neg_domain, _pos_domain)), sub_expr1), And(InSet(l, _full_domain), sub_expr1)).with_wrapping_at(1), InSet(e, _e_domain)))

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())

e \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(\left(l \in \left(\{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\} \cup \{e + 1~\ldotp \ldotp~2^{t - 1}\}\right)\right) \land \left(\left|l\right|_{\textup{mod}\thinspace 2^{t}} > e\right)\right) \\  \Leftrightarrow \left(\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)\right) \end{array} \end{array} \textrm{ if } e \in \{1~\ldotp \ldotp~2^{t - 1} - 2\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 52 body: 2
1	ExprTuple	52
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 20 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	52, 10
8	Operation	operator: 12 operands: 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 40 operands: 14
11	ExprTuple	15, 17
12	Literal
13	ExprTuple	16, 17
14	ExprTuple	63, 18
15	Operation	operator: 20 operands: 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operands: 23
18	Operation	operator: 57 operands: 24
19	ExprTuple	37, 25
20	Literal
21	ExprTuple	37, 26
22	Literal
23	ExprTuple	52, 27
24	ExprTuple	51, 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 40 operands: 31
27	Operation	operator: 32 operands: 33
28	Operation	operator: 61 operand: 55
29	Literal
30	ExprTuple	35, 36
31	ExprTuple	43, 51
32	Literal
33	ExprTuple	37, 38
34	ExprTuple	55
35	Operation	operator: 40 operands: 39
36	Operation	operator: 40 operands: 41
37	Variable
38	Operation	operator: 53 operands: 42
39	ExprTuple	43, 44
40	Literal
41	ExprTuple	48, 51
42	ExprTuple	55, 59
43	Operation	operator: 57 operands: 45
44	Operation	operator: 61 operand: 48
45	ExprTuple	47, 63
46	ExprTuple	48
47	Operation	operator: 61 operand: 51
48	Operation	operator: 57 operands: 50
49	ExprTuple	51
50	ExprTuple	52, 63
51	Operation	operator: 53 operands: 54
52	Variable
53	Literal
54	ExprTuple	55, 56
55	Literal
56	Operation	operator: 57 operands: 58
57	Literal
58	ExprTuple	59, 60
59	Literal
60	Operation	operator: 61 operand: 63
61	Literal
62	ExprTuple	63
63	Literal