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Expression of type Conditional

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 Conditional, 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 = Conditional(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()))), And(InSet(a, Real), InSet(b, 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())
\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) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R}\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 6
2Operationoperator: 26
operands: 5
3Literal
4ExprTuple6
5ExprTuple7, 8
6Lambdaparameter: 36
body: 10
7Operationoperator: 24
operands: 11
8Operationoperator: 24
operands: 12
9ExprTuple36
10Operationoperator: 13
operands: 14
11ExprTuple35, 28
12ExprTuple37, 28
13Literal
14ExprTuple15, 16
15Operationoperator: 24
operands: 17
16Operationoperator: 26
operands: 18
17ExprTuple36, 19
18ExprTuple20, 21
19Operationoperator: 22
operands: 23
20Operationoperator: 24
operands: 25
21Operationoperator: 26
operands: 27
22Literal
23ExprTuple35, 37
24Literal
25ExprTuple36, 28
26Literal
27ExprTuple29, 30
28Literal
29Operationoperator: 31
operands: 32
30Operationoperator: 33
operands: 34
31Literal
32ExprTuple35, 36
33Literal
34ExprTuple36, 37
35Variable
36Variable
37Variable