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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.logic.sets.functions.surjections import surjective_def
In [2]:
# check that the built expression is the same as the stored expression
assert surjective_def.expr == stored_expr
assert surjective_def.expr._style_id == stored_expr._style_id
print("Passed sanity check: surjective_def matches stored_expr")
Passed sanity check: surjective_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}~\left[\forall_{f}~\left(\begin{array}{c} \begin{array}{l} \left(f \in \left[A \xrightarrow[\text{onto}]{} B\right]\right) =  \\ \left(\left(f \in \left[A \rightarrow B\right]\right) \land \left(f^{\rightarrow}(A) = B\right)\right) \end{array} \end{array}\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: 4
operand: 2
1ExprTuple2
2Lambdaparameters: 26
body: 3
3Operationoperator: 4
operand: 6
4Literal
5ExprTuple6
6Lambdaparameter: 30
body: 8
7ExprTuple30
8Operationoperator: 21
operands: 9
9ExprTuple10, 11
10Operationoperator: 19
operands: 12
11Operationoperator: 13
operands: 14
12ExprTuple30, 15
13Literal
14ExprTuple16, 17
15Operationoperator: 18
operands: 26
16Operationoperator: 19
operands: 20
17Operationoperator: 21
operands: 22
18Literal
19Literal
20ExprTuple30, 23
21Literal
22ExprTuple24, 29
23Operationoperator: 25
operands: 26
24Operationoperator: 27
operands: 28
25Literal
26ExprTuple31, 29
27Literal
28ExprTuple30, 31
29Variable
30Variable
31Variable