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Section2.v
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Load Formulas.
Require Import Omega.
Theorem T081a: Problem081aTrue. cbv.
firstorder.
Qed.
Theorem T082a: Problem082aTrue. cbv.
firstorder.
Qed.
Theorem T083a: Problem083aTrue. cbv.
firstorder.
Abort All.
Theorem T083a: Problem083aFalse. cbv.
firstorder.
Abort All.
Transparent PN2object.
Theorem T084a: Problem084aTrue. cbv.
intros contract isContract.
destruct jones_PN as [jones] .
destruct smith_PN as [smith].
destruct anderson_PN as [andersson].
intros.
elim H.
intro.
destruct H0.
Abort All.
(* FIXME: In H, the negation should distribute over 'and' ("narrow scoping") *)
Require Import Psatz.
Theorem T085a: Problem085aFalse.
cbv.
intros contract isContract.
intros [[lawyer [isLawyer [lsigned P1]]] P2].
rewrite -> P1.
intros [l' [isLawyer' [lsigned' H]]].
destruct H.
split.
Qed.
Theorem T086a: Problem086aFalse. cbv.
intros contract isContract.
intros [[lawyer [isLawyer [lsigned P1]]] P2].
rewrite -> P1.
intros [l' [isLawyer' [lsigned' H]]].
destruct H.
split.
Qed.
Theorem T087a: Problem087aTrue. cbv.
firstorder.
Qed.
Theorem T088a: Problem088aTrue. cbv.
intros.
firstorder.
Qed.
Theorem T089a: Problem089aTrue. cbv.
firstorder.
Qed.
Theorem T090a: Problem090aTrue. cbv.
firstorder.
Qed.
Theorem T091a: Problem091aTrue. cbv.
firstorder.
Qed.
Theorem T092a: Problem092aTrue. cbv.
firstorder.
Qed.
Theorem T093a: Problem093aTrue. cbv.
intros theMeeting isMeeting.
intros P.
firstorder.
Qed.
Theorem T094a: Problem094aFalse. cbv. firstorder. Abort All.
Theorem T094a: Problem094aTrue. cbv. firstorder. Qed.
Theorem T095a: Problem095aTrue. cbv. firstorder. Qed.
Theorem T096a: Problem096aTrue. cbv. firstorder. Qed.
Theorem T097a: Problem097aTrue. cbv.
intros theFailure isFailure P1.
firstorder.
Qed.
Theorem T098a: Problem098aTrue. cbv. firstorder. Abort All.
Theorem T098a: Problem098aFalse. cbv. firstorder. Abort All.
Transparent PN2object.
Transparent PN2Class.
Theorem T099a: Problem099aTrue. cbv.
intros theSystem isSystem theDemo isDemo.
intros [P1 P2].
lapply (P1 SMITH).
intros [thePerf [H1 [H2 H3]]].
exists thePerf.
split.
exact H1.
split.
exact SMITH_PERSON.
assumption.
firstorder.
Qed.
Theorem T100a: Problem100aTrue. cbv.
firstorder.
apply most_card_mono1.
firstorder.
Qed.
Variable likely_weakening_K : forall (p:CN) (x:object), p x -> apSubsectiveA likely_A p x.
Theorem T101a: Problem101aTrue. cbv.
firstorder.
apply likely_weakening_K.
firstorder.
exact SMITH_PERSON.
Qed.
Theorem T102a: Problem102aTrue. cbv. firstorder.
Abort All.
Theorem T102a: Problem102aFalse. cbv. firstorder.
Abort All.
Theorem T103a: Problem103aTrue. cbv. firstorder.
Qed.
Theorem T104a: Problem104aTrue. cbv.
firstorder.
Abort All.
Theorem T104a: Problem104aFalse. cbv.
firstorder.
Abort All.
Theorem T105a: Problem105aFalse. cbv.
firstorder.
Qed.
Theorem T106a: Problem106aFalse. cbv.
firstorder.
Qed.
Theorem T107a: Problem107aTrue. cbv.
intros theMeeting isMeeting.
intro P.
firstorder.
Qed.
Theorem T108a: Problem108aTrue. cbv.
firstorder.
Qed.
Theorem T109a: Problem109aFalse. cbv.
Abort All.
(* FIXME "Some" plural ==> card > 1 --- however, this makes many proofs much harder. Try this maybe after we have better automation? *)
Theorem T110a: Problem110aTrue. cbv.
firstorder.
Qed.
Theorem T111a: Problem111aTrue. cbv.
firstorder.
(* incorrect collective reading. *)
Abort All.
Theorem T112a: Problem112aTrue. cbv.
firstorder.
Qed.
Theorem T113a: Problem113aTrue. cbv.
firstorder.
Qed.