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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.natural_numbers import successor_in_nats
In [2]:
# check that the built expression is the same as the stored expression
assert successor_in_nats.expr == stored_expr
assert successor_in_nats.expr._style_id == stored_expr._style_id
print("Passed sanity check: successor_in_nats matches stored_expr")
Passed sanity check: successor_in_nats matches stored_expr
In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(successor_in_nats.latex())
\vdash \forall_{n \in \mathbb{N}}~\left(\left(n + 1\right) \in \mathbb{N}\right)
In [4]:
successor_in_nats.style_options()
Out[4]:
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
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
successor_in_nats.expr_info()
Out[5]:
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameter: 14
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 8
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 11
8Literal
9ExprTuple14, 11
10Operationoperator: 12
operands: 13
11Literal
12Literal
13ExprTuple14, 15
14Variable
15Literal