logo

Expression of type Equals

from the theory of proveit.numbers.modular

In [1]:
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 N, a, b, x
from proveit.logic import Equals, SetOfAll
from proveit.numbers import Interval, Mod, one, subtract, zero
In [2]:
# build up the expression from sub-expressions
expr = Equals(SetOfAll(instance_param_or_params = [x], instance_element = Mod(x, N), domain = Interval(a, b)), Interval(zero, subtract(N, one)))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left\{x ~\textup{mod}~ N\right\}_{x \in \{a~\ldotp \ldotp~b\}} = \{0~\ldotp \ldotp~N - 1\}
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(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')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 5
operand: 8
4Operationoperator: 28
operands: 7
5Literal
6ExprTuple8
7ExprTuple9, 10
8Lambdaparameter: 25
body: 12
9Literal
10Operationoperator: 13
operands: 14
11ExprTuple25
12Conditionalvalue: 15
condition: 16
13Literal
14ExprTuple24, 17
15Operationoperator: 18
operands: 19
16Operationoperator: 20
operands: 21
17Operationoperator: 22
operand: 27
18Literal
19ExprTuple25, 24
20Literal
21ExprTuple25, 26
22Literal
23ExprTuple27
24Variable
25Variable
26Operationoperator: 28
operands: 29
27Literal
28Literal
29ExprTuple30, 31
30Variable
31Variable