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 And, Equals, InSet
from proveit.numbers import Exp, Interval, IntervalCO, Mult, Real, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import var_ket_u
from proveit.physics.quantum.QPE import phase, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = InSet(phase, Real)
sub_expr2 = InSet(Mult(two_pow_t, phase), Interval(zero, subtract(two_pow_t, one)))
sub_expr3 = Equals(MatrixMult(U, var_ket_u), ScalarMult(Exp(e, Mult(two, pi, i, phase)), var_ket_u))
expr = ExprTuple(And(sub_expr1, sub_expr2, sub_expr3), And(sub_expr1, sub_expr2, sub_expr3, InSet(phase, IntervalCO(zero, one))))

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(\left(\varphi \in \mathbb{R}\right) \land \left(\left(2^{t} \cdot \varphi\right) \in \{0~\ldotp \ldotp~2^{t} - 1\}\right) \land \left(\left(U \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert u \rangle\right)\right), \left(\varphi \in \mathbb{R}\right) \land \left(\left(2^{t} \cdot \varphi\right) \in \{0~\ldotp \ldotp~2^{t} - 1\}\right) \land \left(\left(U \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert u \rangle\right)\right) \land \left(\varphi \in \left[0,1\right)\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
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7, 8
4	Literal
5	ExprTuple	6, 7, 8, 9
6	Operation	operator: 14 operands: 10
7	Operation	operator: 14 operands: 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operands: 15
10	ExprTuple	54, 16
11	ExprTuple	17, 18
12	Literal
13	ExprTuple	19, 20
14	Literal
15	ExprTuple	54, 21
16	Literal
17	Operation	operator: 47 operands: 22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 25 operands: 26
20	Operation	operator: 27 operands: 28
21	Operation	operator: 29 operands: 30
22	ExprTuple	39, 54
23	Literal
24	ExprTuple	35, 31
25	Literal
26	ExprTuple	32, 34
27	Literal
28	ExprTuple	33, 34
29	Literal
30	ExprTuple	35, 50
31	Operation	operator: 36 operands: 37
32	Variable
33	Operation	operator: 43 operands: 38
34	Variable
35	Literal
36	Literal
37	ExprTuple	39, 40
38	ExprTuple	41, 42
39	Operation	operator: 43 operands: 44
40	Operation	operator: 45 operand: 50
41	Literal
42	Operation	operator: 47 operands: 48
43	Literal
44	ExprTuple	51, 49
45	Literal
46	ExprTuple	50
47	Literal
48	ExprTuple	51, 52, 53, 54
49	Variable
50	Literal
51	Literal
52	Literal
53	Literal
54	Variable