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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 Add, Ceil, LessEq, Real
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x, y], instance_expr = LessEq(Ceil(Add(x, y)), Add(Ceil(x), Ceil(y))), 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, y \in \mathbb{R}}~\left(\left\lceil x + y\right\rceil \leq \left(\left\lceil x\right\rceil + \left\lceil y\right\rceil\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: 25
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple13, 14
11Operationoperator: 27
operand: 20
12Operationoperator: 24
operands: 16
13Operationoperator: 18
operands: 17
14Operationoperator: 18
operands: 19
15ExprTuple20
16ExprTuple21, 22
17ExprTuple29, 23
18Literal
19ExprTuple30, 23
20Operationoperator: 24
operands: 25
21Operationoperator: 27
operand: 29
22Operationoperator: 27
operand: 30
23Literal
24Literal
25ExprTuple29, 30
26ExprTuple29
27Literal
28ExprTuple30
29Variable
30Variable