# 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 f, i, j
from proveit.core_expr_types import Len, f_i_to_j, iter_ext_equiv
from proveit.logic import Forall, InSet
from proveit.numbers import Natural

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f, i, j], instance_expr = iter_ext_equiv, condition = InSet(Len(operands = [f_i_to_j]), 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())

\forall_{f, i, j~|~|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right)| \in \mathbb{N}}~\left(\begin{array}{c} \begin{array}{l} \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j + 1\right)\right) =  \\ \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right), f\left(j + 1\right)\right) \end{array} \end{array}\right)

In [5]:
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 [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple30, 24, 28
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple12, 13
10Literal
11ExprTuple14, 15
12ExprTuple16
13ExprTuple21, 17
14Operationoperator: 18
operands: 19
15Literal
16ExprRangelambda_map: 23
start_index: 24
end_index: 22
17Operationoperator: 30
operand: 22
18Literal
19ExprTuple21
20ExprTuple22
21ExprRangelambda_map: 23
start_index: 24
end_index: 28
22Operationoperator: 25
operands: 26
23Lambdaparameter: 32
body: 27
24Variable
25Literal
26ExprTuple28, 29
27Operationoperator: 30
operand: 32
28Variable
29Literal
30Variable
31ExprTuple32
32Variable