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, 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
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)), 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(\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)

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, 6
3	Operation	operator: 11 operands: 7
4	Operation	operator: 11 operands: 8
5	Operation	operator: 9 operands: 10
6	Operation	operator: 11 operands: 12
7	ExprTuple	51, 13
8	ExprTuple	14, 15
9	Literal
10	ExprTuple	16, 17
11	Literal
12	ExprTuple	51, 18
13	Literal
14	Operation	operator: 44 operands: 19
15	Operation	operator: 20 operands: 21
16	Operation	operator: 22 operands: 23
17	Operation	operator: 24 operands: 25
18	Operation	operator: 26 operands: 27
19	ExprTuple	36, 51
20	Literal
21	ExprTuple	32, 28
22	Literal
23	ExprTuple	29, 31
24	Literal
25	ExprTuple	30, 31
26	Literal
27	ExprTuple	32, 47
28	Operation	operator: 33 operands: 34
29	Variable
30	Operation	operator: 40 operands: 35
31	Variable
32	Literal
33	Literal
34	ExprTuple	36, 37
35	ExprTuple	38, 39
36	Operation	operator: 40 operands: 41
37	Operation	operator: 42 operand: 47
38	Literal
39	Operation	operator: 44 operands: 45
40	Literal
41	ExprTuple	48, 46
42	Literal
43	ExprTuple	47
44	Literal
45	ExprTuple	48, 49, 50, 51
46	Variable
47	Literal
48	Literal
49	Literal
50	Literal
51	Variable