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 Literal, e, m
from proveit.logic import And, InSet
from proveit.numbers import Exp, Interval, LessEq, ModAbs, one, subtract, two, zero

# build up the expression from sub-expressions
sub_expr1 = Exp(two, Literal("t", theory = "proveit.physics.quantum.QPE"))
expr = And(InSet(m, Interval(zero, subtract(sub_expr1, one))), LessEq(ModAbs(subtract(m, Literal("b_{f}", latex_format = r"b_{\textit{f}}", theory = "proveit.physics.quantum.QPE")), sub_expr1), e))

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(m \in \{0~\ldotp \ldotp~2^{t} - 1\}\right) \land \left(\left|m - b_{\textit{f}}\right|_{\textup{mod}\thinspace 2^{t}} \leq e\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: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	24, 9
7	Literal
8	ExprTuple	10, 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	Variable
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 22
16	Literal
17	Operation	operator: 20 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 29 operand: 33
24	Variable
25	Operation	operator: 29 operand: 34
26	Literal
27	ExprTuple	31, 32
28	ExprTuple	33
29	Literal
30	ExprTuple	34
31	Literal
32	Literal
33	Literal
34	Literal