Expression of type Lambda

from the theory of proveit.physics.quantum.QFT

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, n
from proveit.linear_algebra import Unitary
from proveit.logic import InSet
from proveit.numbers import Exp, NaturalPos, two
from proveit.physics.quantum.QFT import InverseFourierTransform

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(InSet(InverseFourierTransform(n), Unitary(Exp(two, n))), InSet(n, NaturalPos)))

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())

n \mapsto \left\{{\mathrm {FT}}^{\dag}_{n} \in \textrm{U}\left(2^{n}\right) \textrm{ if } n \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 18 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	18, 9
7	Operation	operator: 10 operand: 18
8	Operation	operator: 12 operand: 14
9	Literal
10	Literal
11	ExprTuple	18
12	Literal
13	ExprTuple	14
14	Operation	operator: 15 operands: 16
15	Literal
16	ExprTuple	17, 18
17	Literal
18	Variable