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, Mult, 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(Mult(_two_pow_t, _delta_b), l), 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\{\left(2^{t} \cdot \delta_{b}\right) \neq l \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	33, 23
2	Conditional	value: 3 condition: 4
3	Operation	operator: 17 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 23
6	Literal
7	ExprTuple	9, 10, 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 17 operands: 18
12	Literal
13	ExprTuple	19, 20
14	ExprTuple	33, 21
15	Literal
16	ExprTuple	23, 22
17	Literal
18	ExprTuple	23, 24
19	Operation	operator: 25 operands: 26
20	Operation	operator: 27 operand: 33
21	Operation	operator: 29 operands: 30
22	Literal
23	Variable
24	Literal
25	Literal
26	ExprTuple	31, 32
27	Literal
28	ExprTuple	33
29	Literal
30	ExprTuple	34, 35
31	Literal
32	Literal
33	Variable
34	Literal
35	Literal