Expression of type Lambda

from the theory of proveit.physics.quantum

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, U, x
from proveit.linear_algebra import Unitary
from proveit.logic import InSet
from proveit.numbers import two
from proveit.physics.quantum import Qmult, QubitSpace

# build up the expression from sub-expressions
expr = Lambda(U, Conditional(InSet(Qmult(U, x), QubitSpace), InSet(U, Unitary(two))))

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())

U \mapsto \left\{\left(U \thinspace x\right) \in \mathbb{C}^{2} \textrm{ if } U \in \textrm{U}\left(2\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: 17 body: 2
1	ExprTuple	17
2	Conditional	value: 3 condition: 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	17, 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operand: 20
11	Literal
12	ExprTuple	17, 18
13	Literal
14	ExprTuple	19, 20
15	Literal
16	ExprTuple	20
17	Variable
18	Variable
19	Literal
20	Literal