Expression of type And

from the theory of proveit.physics.quantum.QFT

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 k, l, n
from proveit.logic import And, InSet
from proveit.numbers import Exp, Interval, one, subtract, two, zero

# build up the expression from sub-expressions
sub_expr1 = Interval(zero, subtract(Exp(two, n), one))
expr = And(InSet(k, sub_expr1), InSet(l, sub_expr1))

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(k \in \{0~\ldotp \ldotp~2^{n} - 1\}\right) \land \left(l \in \{0~\ldotp \ldotp~2^{n} - 1\}\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
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 10
6	Literal
7	ExprTuple	9, 10
8	Variable
9	Variable
10	Operation	operator: 11 operands: 12
11	Literal
12	ExprTuple	13, 14
13	Literal
14	Operation	operator: 15 operands: 16
15	Literal
16	ExprTuple	17, 18
17	Operation	operator: 19 operands: 20
18	Operation	operator: 21 operand: 25
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25
23	Literal
24	Variable
25	Literal