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In [1]:
import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_axiom_expr # Load the stored axiom expression as 'stored_expr'
# import the special expression
from proveit.numbers.number_sets.real_numbers import in_IntervalOO_def
In [2]:
# check that the built expression is the same as the stored expression
assert in_IntervalOO_def.expr == stored_expr
assert in_IntervalOO_def.expr._style_id == stored_expr._style_id
print("Passed sanity check: in_IntervalOO_def matches stored_expr")
Passed sanity check: in_IntervalOO_def matches stored_expr
In [3]:
# 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 < b\right)\right)\right)\right]
In [4]:
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 [5]:
# 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: 38
body: 13
10Operationoperator: 27
operands: 14
11Operationoperator: 27
operands: 15
12ExprTuple38
13Operationoperator: 16
operands: 17
14ExprTuple37, 31
15ExprTuple39, 31
16Literal
17ExprTuple18, 19
18Operationoperator: 27
operands: 20
19Operationoperator: 29
operands: 21
20ExprTuple38, 22
21ExprTuple23, 24
22Operationoperator: 25
operands: 26
23Operationoperator: 27
operands: 28
24Operationoperator: 29
operands: 30
25Literal
26ExprTuple37, 39
27Literal
28ExprTuple38, 31
29Literal
30ExprTuple32, 33
31Literal
32Operationoperator: 35
operands: 34
33Operationoperator: 35
operands: 36
34ExprTuple37, 38
35Literal
36ExprTuple38, 39
37Variable
38Variable
39Variable