logo

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 n, x
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Floor, Integer, Real
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x], instance_expr = Forall(instance_param_or_params = [n], instance_expr = Equals(Floor(Add(x, n)), Add(Floor(x), n)), domain = Integer), domain = Real)
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}}~\left[\forall_{n \in \mathbb{Z}}~\left(\left\lfloor x + n\right\rfloor = \left(\left\lfloor x\right\rfloor + n\right)\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: 6
operand: 2
1ExprTuple2
2Lambdaparameter: 31
body: 3
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 9
5Operationoperator: 17
operands: 8
6Literal
7ExprTuple9
8ExprTuple31, 10
9Lambdaparameter: 30
body: 12
10Literal
11ExprTuple30
12Conditionalvalue: 13
condition: 14
13Operationoperator: 15
operands: 16
14Operationoperator: 17
operands: 18
15Literal
16ExprTuple19, 20
17Literal
18ExprTuple30, 21
19Operationoperator: 28
operand: 24
20Operationoperator: 26
operands: 23
21Literal
22ExprTuple24
23ExprTuple25, 30
24Operationoperator: 26
operands: 27
25Operationoperator: 28
operand: 31
26Literal
27ExprTuple31, 30
28Literal
29ExprTuple31
30Variable
31Variable