# from the theory of proveit.core_expr_types.tuples¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, f, i, j
from proveit.core_expr_types import partition_back_equiv
from proveit.logic import InSet
from proveit.numbers import Natural, subtract

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, i, j], Conditional(partition_back_equiv, InSet(subtract(j, i), Natural))))

expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(f, i, j\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right) =  \\ \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j - 1\right), f\left(j\right)\right) \end{array} \end{array} \textrm{ if } \left(j - i\right) \in \mathbb{N}\right..\right)

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 2
body: 3
2ExprTuple26, 30, 28
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10, 11
8Literal
9ExprTuple12, 13
10ExprTuple14
11ExprTuple15, 16
12Operationoperator: 23
operands: 17
13Literal
14ExprRangelambda_map: 18
start_index: 30
end_index: 28
15ExprRangelambda_map: 18
start_index: 30
end_index: 19
16Operationoperator: 26
operand: 28
17ExprTuple28, 21
18Lambdaparameter: 31
body: 22
19Operationoperator: 23
operands: 24
20ExprTuple28
21Operationoperator: 32
operand: 30
22Operationoperator: 26
operand: 31
23Literal
24ExprTuple28, 29
25ExprTuple30
26Variable
27ExprTuple31
28Variable
29Operationoperator: 32
operand: 34
30Variable
31Variable
32Literal
33ExprTuple34
34Literal