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 Forall, InSet
from proveit.numbers import two
from proveit.physics.quantum import Qmult, QubitSpace

# build up the expression from sub-expressions
expr = Lambda(x, Conditional(Forall(instance_param_or_params = [U], instance_expr = InSet(Qmult(U, x), QubitSpace), domain = Unitary(two)), InSet(x, QubitSpace)))

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())

x \mapsto \left\{\forall_{U \in \textrm{U}\left(2\right)}~\left(\left(U \thinspace x\right) \in \mathbb{C}^{2}\right) \textrm{ if } x \in \mathbb{C}^{2}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 26 body: 2
1	ExprTuple	26
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 14 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	26, 17
8	Lambda	parameter: 25 body: 10
9	ExprTuple	25
10	Conditional	value: 11 condition: 12
11	Operation	operator: 14 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	25, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operand: 28
19	Literal
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	27, 28
23	Literal
24	ExprTuple	28
25	Variable
26	Variable
27	Literal
28	Literal