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, a, b
from proveit.logic import And, InSet
from proveit.numbers import Integer
from proveit.physics.quantum.QPE import ModAdd, _m_domain

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(InSet(ModAdd(a, b), _m_domain), And(InSet(a, Integer), InSet(b, Integer))))

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(a, b\right) \mapsto \left\{\left(a \oplus b\right) \in \{0~\ldotp \ldotp~2^{t} - 1\} \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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