Expression of type ExprTuple

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 ExprTuple, U
from proveit.linear_algebra import MatrixMult, ScalarMult
from proveit.logic import Equals, InSet
from proveit.numbers import Exp, IntervalCO, Mult, Real, e, i, one, pi, two, zero
from proveit.physics.quantum import var_ket_u
from proveit.physics.quantum.QPE import phase

# build up the expression from sub-expressions
expr = ExprTuple(InSet(phase, Real), InSet(phase, IntervalCO(zero, one)), Equals(MatrixMult(U, var_ket_u), ScalarMult(Exp(e, Mult(two, pi, i, phase)), var_ket_u)))

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(\varphi \in \mathbb{R}, \varphi \in \left[0,1\right), \left(U \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert u \rangle\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2, 3
1	Operation	operator: 5 operands: 4
2	Operation	operator: 5 operands: 6
3	Operation	operator: 7 operands: 8
4	ExprTuple	33, 9
5	Literal
6	ExprTuple	33, 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 17 operands: 18
13	Literal
14	ExprTuple	19, 20
15	Literal
16	ExprTuple	21, 23
17	Literal
18	ExprTuple	22, 23
19	Literal
20	Literal
21	Variable
22	Operation	operator: 24 operands: 25
23	Variable
24	Literal
25	ExprTuple	26, 27
26	Literal
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31, 32, 33
30	Literal
31	Literal
32	Literal
33	Variable