# 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.
# import Expression classes needed to build the expression
from proveit import f, i, j, x
from proveit.core_expr_types import Len, f_i_to_j
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Natural, Neg, two

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f, x], instance_expr = Forall(instance_param_or_params = [i, j], instance_expr = Equals(Len(operands = [f_i_to_j, x]), Add(j, Neg(i), two)), 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, x}~\left[\forall_{i, j~|~|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right)| \in \mathbb{N}}~\left(|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right), x\right)| = \left(j - i + 2\right)\right)\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: 5
operand: 2
1ExprTuple2
2Lambdaparameters: 3
body: 4
3ExprTuple35, 25
4Operationoperator: 5
operand: 7
5Literal
6ExprTuple7
7Lambdaparameters: 8
body: 9
8ExprTuple33, 32
9Conditionalvalue: 10
condition: 11
10Operationoperator: 12
operands: 13
11Operationoperator: 14
operands: 15
12Literal
13ExprTuple16, 17
14Literal
15ExprTuple18, 19
16Operationoperator: 23
operands: 20
17Operationoperator: 21
operands: 22
18Operationoperator: 23
operands: 24
19Literal
20ExprTuple28, 25
21Literal
22ExprTuple32, 26, 27
23Literal
24ExprTuple28
25Variable
26Operationoperator: 29
operand: 33
27Literal
28ExprRangelambda_map: 31
start_index: 33
end_index: 32
29Literal
30ExprTuple33
31Lambdaparameter: 37
body: 34
32Variable
33Variable
34Operationoperator: 35
operand: 37
35Variable
36ExprTuple37
37Variable