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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_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.numbers.summation import summation_int_closure
In [2]:
# check that the built expression is the same as the stored expression
assert summation_int_closure.expr == stored_expr
assert summation_int_closure.expr._style_id == stored_expr._style_id
print("Passed sanity check: summation_int_closure matches stored_expr")
Passed sanity check: summation_int_closure matches stored_expr
In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\forall_{f, Q}~\left(\left[\forall_{x~|~Q\left(x\right)}~\left(f\left(x\right) \in \mathbb{Z}\right)\right] \Rightarrow \left(\left[\sum_{x~|~Q\left(x\right)}~f\left(x\right)\right] \in \mathbb{Z}\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: 9
operand: 2
1ExprTuple2
2Lambdaparameters: 3
body: 4
3ExprTuple25, 26
4Operationoperator: 5
operands: 6
5Literal
6ExprTuple7, 8
7Operationoperator: 9
operand: 12
8Operationoperator: 19
operands: 11
9Literal
10ExprTuple12
11ExprTuple13, 22
12Lambdaparameter: 28
body: 14
13Operationoperator: 15
operand: 18
14Conditionalvalue: 17
condition: 24
15Literal
16ExprTuple18
17Operationoperator: 19
operands: 20
18Lambdaparameter: 28
body: 21
19Literal
20ExprTuple23, 22
21Conditionalvalue: 23
condition: 24
22Literal
23Operationoperator: 25
operand: 28
24Operationoperator: 26
operand: 28
25Variable
26Variable
27ExprTuple28
28Variable