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Expression of type Forall

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, x
from proveit.logic import And, Equals, Forall
from proveit.numbers import LessEq, ModAbs, Real, RealPos, frac, two, zero
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x, N], instance_expr = Equals(ModAbs(x, N), x), domains = [Real, RealPos], condition = And(LessEq(zero, x), LessEq(x, frac(N, two))).with_total_ordering_style())
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())
\forall_{x \in \mathbb{R}, N \in \mathbb{R}^+~|~0 \leq x \leq \frac{N}{2}}~\left(\left|x\right|_{\textup{mod}\thinspace N} = x\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 15
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 19
operands: 9
7Literal
8ExprTuple10, 29
9ExprTuple11, 12, 13
10Operationoperator: 14
operands: 15
11Operationoperator: 17
operands: 16
12Operationoperator: 17
operands: 18
13Operationoperator: 19
operands: 20
14Literal
15ExprTuple29, 33
16ExprTuple29, 21
17Literal
18ExprTuple33, 22
19Literal
20ExprTuple23, 24
21Literal
22Literal
23Operationoperator: 26
operands: 25
24Operationoperator: 26
operands: 27
25ExprTuple28, 29
26Literal
27ExprTuple29, 30
28Literal
29Variable
30Operationoperator: 31
operands: 32
31Literal
32ExprTuple33, 34
33Variable
34Literal