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Expression of type ExprTuple

from the theory of proveit.logic.booleans.disjunction

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, ExprRange, ExprTuple, Function, Lambda, P, Pk, Variable, i, j, k
from proveit.logic import Equals, Exists, Or
from proveit.numbers import Add, Interval, LessEq, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda(P, Conditional(Equals(Or(ExprRange(sub_expr1, Function(P, [sub_expr1]), i, j)), Exists(instance_param_or_params = [k], instance_expr = Pk, domain = Interval(i, j))), LessEq(i, Add(j, one)))))
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(P \mapsto \left\{\left(P\left(i\right) \lor  P\left(i + 1\right) \lor  \ldots \lor  P\left(j\right)\right) = \left[\exists_{k \in \{i~\ldotp \ldotp~j\}}~P\left(k\right)\right] \textrm{ if } i \leq \left(j + 1\right)\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
1Lambdaparameter: 28
body: 3
2ExprTuple28
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10, 11
8Literal
9ExprTuple37, 12
10Operationoperator: 13
operands: 14
11Operationoperator: 15
operand: 20
12Operationoperator: 17
operands: 18
13Literal
14ExprTuple19
15Literal
16ExprTuple20
17Literal
18ExprTuple38, 21
19ExprRangelambda_map: 22
start_index: 37
end_index: 38
20Lambdaparameter: 33
body: 23
21Literal
22Lambdaparameter: 32
body: 24
23Conditionalvalue: 25
condition: 26
24Operationoperator: 28
operand: 32
25Operationoperator: 28
operand: 33
26Operationoperator: 30
operands: 31
27ExprTuple32
28Variable
29ExprTuple33
30Literal
31ExprTuple33, 34
32Variable
33Variable
34Operationoperator: 35
operands: 36
35Literal
36ExprTuple37, 38
37Variable
38Variable