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.logic import And
from proveit.numbers import Floor, LessEq, Mult, zero
from proveit.physics.quantum.QPE import _phase, _two_pow_t, _two_pow_t__minus_one

# build up the expression from sub-expressions
sub_expr1 = Floor(Mult(_two_pow_t, _phase))
expr = And(LessEq(zero, sub_expr1), LessEq(sub_expr1, _two_pow_t__minus_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(0 \leq \left\lfloor 2^{t} \cdot \varphi\right\rfloor\right) \land \left(\left\lfloor 2^{t} \cdot \varphi\right\rfloor \leq \left(2^{t} - 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',)
as_total_ordering	When 'True', style the conjunction as a total ordering (e.g. x < y < z from (x < y) and (y < z))	None	None/False	('with_total_ordering_style',)

# 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
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	9, 10
8	Literal
9	Operation	operator: 11 operand: 15
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15
13	Literal
14	ExprTuple	21, 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operand: 23
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23
21	Operation	operator: 24 operands: 25
22	Literal
23	Literal
24	Literal
25	ExprTuple	26, 27
26	Literal
27	Literal