Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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())

\left(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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 27 body: 3
2	ExprTuple	27
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 15 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	27, 18
9	Lambda	parameter: 26 body: 11
10	ExprTuple	26
11	Conditional	value: 12 condition: 13
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	26, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operand: 29
20	Literal
21	ExprTuple	26, 27
22	Literal
23	ExprTuple	28, 29
24	Literal
25	ExprTuple	29
26	Variable
27	Variable
28	Literal
29	Literal