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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 = [a, b], instance_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()))), 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_{a, b \in \mathbb{R}}~\left[\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)\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
2Lambdaparameters: 26
body: 3
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 9
5Operationoperator: 29
operands: 8
6Literal
7ExprTuple9
8ExprTuple10, 11
9Lambdaparameter: 39
body: 13
10Operationoperator: 27
operands: 14
11Operationoperator: 27
operands: 15
12ExprTuple39
13Operationoperator: 16
operands: 17
14ExprTuple38, 31
15ExprTuple40, 31
16Literal
17ExprTuple18, 19
18Operationoperator: 27
operands: 20
19Operationoperator: 29
operands: 21
20ExprTuple39, 22
21ExprTuple23, 24
22Operationoperator: 25
operands: 26
23Operationoperator: 27
operands: 28
24Operationoperator: 29
operands: 30
25Literal
26ExprTuple38, 40
27Literal
28ExprTuple39, 31
29Literal
30ExprTuple32, 33
31Literal
32Operationoperator: 34
operands: 35
33Operationoperator: 36
operands: 37
34Literal
35ExprTuple38, 39
36Literal
37ExprTuple39, 40
38Variable
39Variable
40Variable