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, b, l
from proveit.logic import And, InSet, NotEquals, Set
from proveit.numbers import Integer, frac, zero
from proveit.physics.quantum.QPE import _b_floor, _b_round, _delta_b, _two_pow_t

# build up the expression from sub-expressions
expr = Lambda([b, l], Conditional(NotEquals(_delta_b, frac(l, _two_pow_t)), And(InSet(b, Set(_b_floor, _b_round)), InSet(l, Integer), NotEquals(l, zero))))

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(b, l\right) \mapsto \left\{\delta_{b} \neq \frac{l}{2^{t}} \textrm{ if } b \in \left\{b_{\textit{f}}, b_{\textit{r}}\right\} ,  l \in \mathbb{Z} ,  l \neq 0\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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