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
from proveit.logic import Equals, InSet, NotInSet, Or, 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
sub_expr1 = Mult(_two_pow_t, _delta_b)
expr = Lambda(b, Conditional(Or(Equals(sub_expr1, zero), NotInSet(sub_expr1, Integer)), InSet(b, Set(_b_floor, _b_round))))

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())

b \mapsto \left\{\left(\left(2^{t} \cdot \delta_{b}\right) = 0\right) \lor \left(\left(2^{t} \cdot \delta_{b}\right) \notin \mathbb{Z}\right) \textrm{ if } b \in \left\{b_{\textit{f}}, b_{\textit{r}}\right\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 32 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	32, 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operands: 16
11	Literal
12	ExprTuple	18, 17
13	Literal
14	ExprTuple	18, 19
15	Literal
16	ExprTuple	20, 21
17	Literal
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	Literal
22	Literal
23	ExprTuple	24, 25
24	Operation	operator: 26 operands: 27
25	Operation	operator: 28 operand: 32
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32
30	Literal
31	Literal
32	Variable