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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 natural_pos_def
In [2]:
# check that the built expression is the same as the stored expression
assert natural_pos_def.expr == stored_expr
assert natural_pos_def.expr._style_id == stored_expr._style_id
print("Passed sanity check: natural_pos_def matches stored_expr")
Passed sanity check: natural_pos_def matches stored_expr
In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(natural_pos_def.latex())
\vdash \mathbb{N}^+ = \left\{n~|~n > 0\right\}_{n \in \mathbb{N}}
In [4]:
natural_pos_def.style_options()
Out[4]:
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [5]:
# display the expression information
natural_pos_def.expr_info()
Out[5]:
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Literal
4Operationoperator: 5
operand: 7
5Literal
6ExprTuple7
7Lambdaparameter: 20
body: 8
8Conditionalvalue: 20
condition: 9
9Operationoperator: 10
operands: 11
10Literal
11ExprTuple12, 13
12Operationoperator: 14
operands: 15
13Operationoperator: 16
operands: 17
14Literal
15ExprTuple20, 18
16Literal
17ExprTuple19, 20
18Literal
19Literal
20Variable