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 InSet, Set
from proveit.numbers import IntervalOO, Mult, Neg, one
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, Conditional(InSet(Mult(_two_pow_t, _delta_b), IntervalOO(Neg(one), one)), 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(2^{t} \cdot \delta_{b}\right) \in \left(-1,1\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: 29 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	29, 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operands: 15
10	Literal
11	ExprTuple	16, 17
12	Literal
13	ExprTuple	18, 30
14	Literal
15	ExprTuple	19, 20
16	Operation	operator: 21 operands: 22
17	Operation	operator: 23 operand: 29
18	Operation	operator: 25 operand: 30
19	Literal
20	Literal
21	Literal
22	ExprTuple	27, 28
23	Literal
24	ExprTuple	29
25	Literal
26	ExprTuple	30
27	Literal
28	Literal
29	Variable
30	Literal