logo

Expression of type Forall

from the theory of proveit.numbers.number_sets.real_numbers

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 a, b, x
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import IntervalOC, Less, LessEq, Real
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x], instance_expr = Equals(InSet(x, IntervalOC(a, b)), And(InSet(x, Real), And(Less(a, x), LessEq(x, b)).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}~\left(\left(x \in \left(a,b\right]\right) = \left(\left(x \in \mathbb{R}\right) \land \left(a < x \leq b\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: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameter: 29
body: 5
4ExprTuple29
5Operationoperator: 6
operands: 7
6Literal
7ExprTuple8, 9
8Operationoperator: 17
operands: 10
9Operationoperator: 19
operands: 11
10ExprTuple29, 12
11ExprTuple13, 14
12Operationoperator: 15
operands: 16
13Operationoperator: 17
operands: 18
14Operationoperator: 19
operands: 20
15Literal
16ExprTuple28, 30
17Literal
18ExprTuple29, 21
19Literal
20ExprTuple22, 23
21Literal
22Operationoperator: 24
operands: 25
23Operationoperator: 26
operands: 27
24Literal
25ExprTuple28, 29
26Literal
27ExprTuple29, 30
28Variable
29Variable
30Variable