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, l
from proveit.logic import Equals, InSet
from proveit.numbers import Abs, ModAbs
from proveit.physics.quantum.QPE import _full_domain, _two_pow_t

# build up the expression from sub-expressions
expr = Lambda(l, Conditional(Equals(ModAbs(l, _two_pow_t), Abs(l)), InSet(l, _full_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())

l \mapsto \left\{\left|l\right|_{\textup{mod}\thinspace 2^{t}} = \left|l\right| \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 18 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	18, 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operand: 18
10	Operation	operator: 15 operands: 16
11	Literal
12	ExprTuple	18, 17
13	Literal
14	ExprTuple	18
15	Literal
16	ExprTuple	19, 24
17	Operation	operator: 25 operands: 20
18	Variable
19	Operation	operator: 29 operands: 21
20	ExprTuple	27, 31
21	ExprTuple	22, 35
22	Operation	operator: 33 operand: 24
23	ExprTuple	24
24	Operation	operator: 25 operands: 26
25	Literal
26	ExprTuple	27, 28
27	Literal
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	31, 32
31	Literal
32	Operation	operator: 33 operand: 35
33	Literal
34	ExprTuple	35
35	Literal