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products/Sources/formale Sprachen/Isabelle/HOL/Nitpick_Examples/ (Beweissystem Isabelle Version 2025-1^©) Datei vom 16.11.2025 mit Größe 6 kB

Quelle Integer_Nits.thy Sprache: Isabelle

(*  Title:      HOL/Nitpick_Examples/Integer_Nits.thy
    Author:     Jasmin Blanchette, TU Muenchen
    Copyright   2009-2012

Examples featuring Nitpick applied to natural numbers and integers.
*)

section \<open>Examples Featuring Nitpick Applied to Natural Numbers and Integers\<close>

theory Integer_Nits
imports Main
begin

nitpick_params [verbose, card = 1-5, bits = 1,2,3,4,6,
                sat_solver = MiniSat, max_threads = 1, timeout = 240]

lemma "Suc x = x + 1"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "x < Suc x"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "x + y \ (x::nat)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "y \ 0 \ x + y > (x::nat)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "x + y = y + (x::nat)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "x > y \ x - y \ (0::nat)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "x \ y \ x - y = (0::nat)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "x - (0::nat) = x"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "\x \ 0; y \ 0\ \ x * y \ (0::nat)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "0 * y = (0::nat)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "y * 0 = (0::nat)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "\x \ 0; y \ 0\ \ x * y \ (x::nat)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "\x \ 0; y \ 0\ \ x * y \ (y::nat)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "x * y div y = (x::nat)"
nitpick [unary_ints, expect = genuine]
nitpick [binary_ints, expect = genuine]
oops

lemma "y \ 0 \ x * y div y = (x::nat)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "5 * 55 < (260::nat)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
nitpick [binary_ints, bits = 9, expect = genuine]
oops

lemma "nat (of_nat n) = n"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "x + y \ (x::int)"
nitpick [unary_ints, expect = genuine]
nitpick [binary_ints, expect = genuine]
oops

lemma "\x \ 0; y \ 0\ \ x + y \ (0::int)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "y \ 0 \ x + y \ (x::int)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "x \ 0 \ x + y \ (y::int)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "x \ 0 \ x + y \ (x::int)"
nitpick [unary_ints, expect = genuine]
nitpick [binary_ints, expect = genuine]
oops

lemma "\x \ 0; y \ 0\ \ x + y \ (0::int)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "y \ 0 \ x + y > (x::int)"
nitpick [unary_ints, expect = genuine]
nitpick [binary_ints, expect = genuine]
oops

lemma "x + y = y + (x::int)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "x > y \ x - y \ (0::int)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "x \ y \ x - y = (0::int)"
nitpick [unary_ints, expect = genuine]
nitpick [binary_ints, expect = genuine]
oops

lemma "x - (0::int) = x"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "\x \ 0; y \ 0\ \ x * y \ (0::int)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "0 * y = (0::int)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "y * 0 = (0::int)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "\x \ 0; y \ 0\ \ x * y \ (x::int)"
nitpick [unary_ints, expect = genuine]
nitpick [binary_ints, expect = genuine]
oops

lemma "\x \ 0; y \ 0\ \ x * y \ (y::int)"
nitpick [unary_ints, expect = genuine]
nitpick [binary_ints, expect = genuine]
oops

lemma "x * y div y = (x::int)"
nitpick [unary_ints, expect = genuine]
nitpick [binary_ints, expect = genuine]
oops

lemma "y \ 0 \ x * y div y = (x::int)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, card = 1-4, bits = 1-4, expect = none]
sorry

lemma "(x * y < 0) \ (x > 0 \ y < 0) \ (x < 0 \ y > (0::int))"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

lemma "-5 * 55 > (-260::int)"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
nitpick [binary_ints, bits = 9, expect = genuine]
oops

lemma "nat (of_nat n) = n"
nitpick [unary_ints, expect = none]
nitpick [binary_ints, expect = none]
sorry

datatype tree = Null | Node nat tree tree

primrec labels where
"labels Null = {}" |
"labels (Node x t u) = {x} \ labels t \ labels u"

lemma "labels (Node x t u) \ labels (Node y v w)"
nitpick [expect = potential] (* unfortunate *)
oops

lemma "labels (Node x t u) \ {}"
nitpick [expect = none]
oops

lemma "card (labels t) > 0"
nitpick [expect = potential] (* unfortunate *)
oops

lemma "(\n \ labels t. n + 2) \ 2"
nitpick [expect = potential] (* unfortunate *)
oops

lemma "t \ Null \ (\n \ labels t. n + 2) \ 2"
nitpick [expect = potential] (* unfortunate *)
sorry

lemma "(\i \ labels (Node x t u). f i::nat) = f x + (\i \ labels t. f i) + (\i \ labels u. f i)"
nitpick [expect = potential] (* unfortunate *)
oops

end

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