Expression of type And

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 U
from proveit.linear_algebra import MatrixMult, ScalarMult
from proveit.logic import And, Equals, InSet
from proveit.numbers import Exp, Interval, 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
expr = And(InSet(phase, Real), InSet(Mult(two_pow_t, phase), Interval(zero, subtract(two_pow_t, 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}\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)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4, 5
3	Operation	operator: 7 operands: 6
4	Operation	operator: 7 operands: 8
5	Operation	operator: 9 operands: 10
6	ExprTuple	46, 11
7	Literal
8	ExprTuple	12, 13
9	Literal
10	ExprTuple	14, 15
11	Literal
12	Operation	operator: 39 operands: 16
13	Operation	operator: 17 operands: 18
14	Operation	operator: 19 operands: 20
15	Operation	operator: 21 operands: 22
16	ExprTuple	31, 46
17	Literal
18	ExprTuple	23, 24
19	Literal
20	ExprTuple	25, 27
21	Literal
22	ExprTuple	26, 27
23	Literal
24	Operation	operator: 28 operands: 29
25	Variable
26	Operation	operator: 35 operands: 30
27	Variable
28	Literal
29	ExprTuple	31, 32
30	ExprTuple	33, 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 37 operand: 42
33	Literal
34	Operation	operator: 39 operands: 40
35	Literal
36	ExprTuple	43, 41
37	Literal
38	ExprTuple	42
39	Literal
40	ExprTuple	43, 44, 45, 46
41	Variable
42	Literal
43	Literal
44	Literal
45	Literal
46	Variable