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Expression of type Forall

from the theory of proveit.numbers.rounding

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 x, y
from proveit.logic import Forall
from proveit.numbers import Abs, Integer, LessEq, Real, Round, subtract
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x, y], instance_expr = LessEq(Abs(subtract(Round(x), x)), Abs(subtract(y, x))), domains = [Real, Integer])
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}, y \in \mathbb{Z}}~\left(\left|round\left(x\right) - x\right| \leq \left|y - x\right|\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: 4
body: 5
4ExprTuple35, 30
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple12, 13
10Literal
11ExprTuple14, 15
12Operationoperator: 17
operand: 22
13Operationoperator: 17
operand: 23
14Operationoperator: 20
operands: 19
15Operationoperator: 20
operands: 21
16ExprTuple22
17Literal
18ExprTuple23
19ExprTuple35, 24
20Literal
21ExprTuple30, 25
22Operationoperator: 27
operands: 26
23Operationoperator: 27
operands: 28
24Literal
25Literal
26ExprTuple29, 31
27Literal
28ExprTuple30, 31
29Operationoperator: 32
operand: 35
30Variable
31Operationoperator: 33
operand: 35
32Literal
33Literal
34ExprTuple35
35Variable