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
from proveit.numbers import Integer, frac, subtract
from proveit.physics.quantum.QPE import _delta_b, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = Lambda(b, Conditional(Equals(_delta_b, subtract(_phase, frac(b, _two_pow_t))), 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())

b \mapsto \left\{\delta_{b} = \left(\varphi - \frac{b}{2^{t}}\right) \textrm{ if } 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	parameter: 22 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	22, 10
8	Operation	operator: 11 operand: 22
9	Operation	operator: 13 operands: 14
10	Literal
11	Literal
12	ExprTuple	22
13	Literal
14	ExprTuple	15, 16
15	Literal
16	Operation	operator: 17 operand: 19
17	Literal
18	ExprTuple	19
19	Operation	operator: 20 operands: 21
20	Literal
21	ExprTuple	22, 23
22	Variable
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26, 27
26	Literal
27	Literal