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Section1.v
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Section1.v
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Load Formulas.
Theorem T001a: Problem001aTrue. cbv. firstorder. Qed.
Theorem T002a: Problem002aTrue.
cbv. destruct great_A as [great].
intro H.
destruct H as [H1 [x [H2 H3]]].
exists x.
split.
split.
exact H2.
assert (H' := H1 x H2).
generalize H'.
apply wantCovariant_K.
intro H4.
exists x.
split.
exact H4.
split.
split.
Qed.
Theorem T003a: Problem003aTrue.
cbv.
destruct great_A as [great].
firstorder.
Qed.
Theorem T004a: Problem004aTrue.
cbv.
firstorder.
Qed.
Theorem T005a: Problem005aTrue.
cbv.
firstorder.
Abort All.
(* JP: I disagree with FraCaS *)
Theorem T005a: Problem005aFalse.
cbv.
firstorder.
Abort All.
Theorem T006a: Problem006aFalse.
cbv.
destruct great_A as [great].
firstorder.
Qed.
Theorem T007a: Problem007aTrue.
cbv.
firstorder.
Qed.
Theorem T008a: Problem008aTrue. cbv. firstorder. Qed.
Theorem T009a: Problem009aTrue. cbv. firstorder. Qed.
Theorem T010a: Problem010aTrue. cbv.
destruct great_A as [great]. firstorder.
Qed.
Theorem T011a: Problem011aTrue. cbv.
destruct great_A as [great].
firstorder. Qed.
Theorem T013a: Problem013aTrue. cbv.
destruct leading_A as [leading].
destruct indispensable_A as [indispensable].
destruct excellent_A as [excellent].
(* SLOW: firstorder. exists x0. firstorder. exists x1. firstorder.*)
Abort All.
(* FIXME: we're missing indispensable (excellent x) => indispensable x.
There seem to be a subltety about the kind of adjectives.
*)
Theorem T014a: Problem014aFalse. cbv.
destruct leading_A as [leading].
intros [P1 P2] H.
destruct H.
firstorder.
Abort All.
(* FIXME: one of the ... has a syntax which is difficult to interpret; P2 incorrect *)
Theorem T015a: Problem015aTrue. cbv. firstorder. Qed.
Theorem T016a: Problem016aTrue. cbv.
firstorder.
Abort All. (* Undef problem; unresolved reference in P1 *)
Theorem T017a: Problem017aTrue. cbv.
intro the_nobel_prize.
intros H P1.
destruct H as [literature [isLiterature isNobelPrize]].
destruct P1 as [irishman [isIrish hasWon]].
exists irishman.
split.
assumption.
exists the_nobel_prize.
split.
exists literature.
assumption.
assumption.
Qed.
Theorem T018a: Problem018aTrue. cbv. firstorder. Qed.
Theorem T019a: Problem019aTrue. cbv. firstorder. Qed.
Theorem T020a: Problem020aTrue. cbv. firstorder. Qed.
Theorem T021a: Problem021aTrue. cbv.
destruct in_Prep as [inP inV inC].
destruct within_Prep as [within withinVerid withinCov].
destruct europe_PN as [europe regionN].
intros theRTLiE isRTLiE [P1 [P2 P3]].
firstorder.
apply P3.
firstorder.
Qed.
Theorem T022a: Problem022aTrue. cbv. firstorder. Abort All.
Theorem T022a: Problem022aFalse. cbv. firstorder. Abort All.
Theorem T023a: Problem023aTrue. cbv.
destruct on_time_Adv. firstorder. Qed.
Theorem T024a: Problem024aTrue. cbv.
intros.
firstorder.
generalize H0.
apply le_mono_right.
firstorder.
Qed.
Theorem T025a: Problem025aTrue. cbv.
destruct major_A as [major] eqn:majorEq.
destruct national_A as [national] eqn:nationalEq.
destruct in_Prep as [inPrep inVerid inVeridCov].
intros [[Pcard Pexist] Pc].
clear Pc.
destruct Pexist as [delegate [isDelegate [newsPaper [isNewsPaper gotIn]]]].
split.
split.
generalize Pcard.
apply le_mono_right.
intros deleg' [isDeleg [paper [isNewsPaper' gotIn']]].
split.
assumption.
intros result [isresult [somewhere [triv isPublished]]].
apply getInK with (newsPaper := paper).
firstorder.
exists delegate.
split.
assumption.
intros result [isresult [somewhere [triv isPublished]]].
apply getInK with (newsPaper := newsPaper).
firstorder.
firstorder.
Qed.
Theorem T026a: Problem026aTrue. cbv.
firstorder.
generalize H.
apply le_mono_right.
intros european [isEuropean [isResident _]].
lapply (H2 european).
intros canTravel.
split.
assumption.
assumption.
split.
apply H1.
assumption.
split.
assumption.
split.
Qed.
Theorem T027a: Problem027aTrue. cbv.
firstorder.
generalize H.
apply le_mono_right.
firstorder.
Qed.
Theorem T028a: Problem028aTrue. cbv.
firstorder.
generalize H.
apply le_mono_left.
firstorder.
Abort All.
Theorem T028a: Problem028aFalse. cbv.
firstorder.
Abort All.
Theorem T029a: Problem029aTrue. cbv.
firstorder. destruct leading_A as [leading].
exists x.
firstorder.
exists x0.
firstorder.
generalize H1.
apply usedToBeCov_K.
firstorder.
generalize H2.
apply usedToBeCov_K.
firstorder.
Qed.
Theorem T030a: Problem030aTrue. cbv.
intros. destruct at_home_Adv. (* SLOW: firstorder.
exists x0.
split.
assumption.
exists x1. firstorder. apply H3. *)
Abort All.
Theorem T030a': Problem030aFalse. cbv.
destruct at_home_Adv.
(* firstorder. *)
Abort All.
Theorem T031a: Problem031aTrue. cbv.
destruct at_home_Adv as [atHome atHomeVerid].
destruct atHomeVerid as [atHomeVerid atHomeVeridCov].
firstorder.
exists x.
firstorder.
generalize H1. apply le_mono_right. firstorder.
Qed.
Theorem T032a: Problem032aTrue. cbv.
destruct at_home_Adv as [atHome verid].
firstorder.
generalize H.
apply le_mono_left.
intro commiss.
(* firstorder. *)
Abort All.
Theorem T032a: Problem032aFalse. cbv.
destruct at_home_Adv as [atHome verid].
(* firstorder. *)
Abort All.
Theorem T033a: Problem033aTrue. cbv.
(* firstorder. *)
Abort All.
Theorem T033a: Problem033aFalse. cbv.
(* firstorder. *)
Abort All.
Theorem T034a: Problem034aTrue. cbv.
(* firstorder. *)
Abort All.
Theorem T034a: Problem034aFalse. cbv.
(* firstorder. *)
Abort All.
Theorem T035a: Problem035aTrue. cbv.
(* firstorder. *)
Abort All.
Theorem T035a: Problem035aFalse. cbv.
(* firstorder. *)
Abort All.
Theorem T036a: Problem036aTrue. cbv.
(* firstorder. *)
Abort All.
Theorem T036a: Problem036aFalse. cbv.
(* firstorder. *)
Abort All.
Theorem T037a: Problem037aTrue. cbv.
(* firstorder. *)
Abort All.
Theorem T037a: Problem037aFalse. cbv.
(* firstorder. *)
Abort All.
Theorem T038a: Problem038aFalse. cbv.
destruct on_time_Adv as [adv verid].
firstorder.
Qed.
Theorem T039a: Problem039aTrue. cbv.
destruct on_time_Adv as [adv verid].
(* firstorder. *)
Abort All.
Theorem T039a: Problem039aFalse. cbv.
destruct on_time_Adv as [adv verid].
(* firstorder. *)
Abort All.
Theorem T040a: Problem040aTrue. cbv.
destruct on_time_Adv as [adv verid].
firstorder.
generalize H0.
apply le_mono_right.
(* firstorder. *)
Abort All.
Theorem T040a: Problem040aFalse. cbv.
firstorder.
Abort All.
Theorem T041a: Problem041aTrue. cbv.
destruct major_A as [major] eqn:majorEq.
destruct national_A as [national] eqn:nationalEq.
firstorder.
generalize H.
apply le_mono_right.
firstorder.
Abort All.
Theorem T041a: Problem041aFalse. cbv.
destruct major_A as [major] eqn:majorEq.
destruct national_A as [national] eqn:nationalEq.
(*firstorder.*)
Abort All.
Theorem T042a: Problem042aTrue. cbv.
(*firstorder.*)
Abort All.
Theorem T042a: Problem042aFalse. cbv.
(*firstorder.*)
Abort All.
Theorem T043a: Problem043aTrue. cbv.
(*firstorder.*)
Abort All.
Theorem T043a: Problem043aFalse. cbv.
(*firstorder.*)
Abort All.
Theorem T044a: Problem044aTrue. cbv.
firstorder.
generalize H.
apply le_mono_left.
firstorder.
Qed.
Theorem T045a: Problem045aTrue. cbv.
destruct leading_A as [leading].
(* firstorder. *)
Abort All.
Theorem T045a: Problem045aFalse. cbv.
destruct leading_A as [leading].
(* firstorder. *)
Abort All.
Theorem T046a: Problem046aFalse. cbv.
destruct at_home_Adv as [atHome [atHomeVerid atHomeVeridCov]].
intros P1 H.
destruct P1 as [comis1 [isComis [comis2 [isComis2 [notime1 [notime2 noEq]]]]] ].
(* "one of the" syntax difficult to interpret. *)
Abort All.
Theorem T047a: Problem047aTrue. cbv.
destruct at_home_Adv as [atHome [atHomeVerid atHomeVeridCov]].
firstorder.
exists x.
firstorder.
Abort All.
Theorem T047a: Problem047aFalse. cbv.
destruct at_home_Adv as [atHome [atHomeVerid atHomeVeridCov]].
(* firstorder. *)
Abort All.
Theorem T048a: Problem048aTrue. cbv.
apply le_mono_left.
firstorder.
Qed.
Theorem T049a: Problem049aTrue. cbv.
firstorder.
Qed.
Theorem T050a: Problem050aTrue. cbv.
firstorder.
Abort All.
Theorem T050a: Problem050aFalse. cbv.
firstorder.
Abort All.
Theorem T051a: Problem051aTrue. cbv.
firstorder.
Abort All.
Theorem T051a: Problem051aFalse. cbv.
firstorder.
Abort All.
Theorem T052a: Problem052aTrue. cbv.
firstorder.
Abort All.
Theorem T052a: Problem052aFalse. cbv.
firstorder.
Abort All.
Theorem T053a: Problem053aTrue. cbv.
firstorder.
Abort All.
Theorem T053a: Problem053aFalse. cbv.
firstorder.
Abort All.
Theorem T054a: Problem054aTrue. cbv.
firstorder.
Abort All.
Theorem T054a: Problem054aFalse. cbv.
firstorder.
Abort All.
Theorem T055a: Problem055aTrue. cbv.
firstorder.
Qed.
Theorem T056a: Problem056aTrue. cbv.
firstorder.
generalize H0.
apply le_mono_right.
firstorder.
Qed. (* See note in the xml *)
Theorem T057a: Problem057aTrue. cbv.
destruct major_A as [major] eqn:majorEq.
destruct national_A as [national] eqn:nationalEq.
firstorder.
generalize H.
apply le_mono_right.
firstorder.
Qed.
Theorem T058a: Problem058aTrue. cbv.
firstorder.
generalize H.
Abort All.
Theorem T058a: Problem058aFalse. cbv.
firstorder.
Abort All.
Theorem T059a: Problem059aTrue. cbv.
firstorder.
generalize H.
apply le_mono_right.
firstorder.
Qed.
Theorem T060a: Problem060aTrue. cbv.
firstorder.
generalize H.
apply le_mono_left.
firstorder.
Abort All.
Theorem T060a: Problem060aFalse. cbv.
firstorder.
Abort All.
Theorem T063a: Problem063aTrue. cbv.
firstorder.
exists x.
firstorder.
generalize H1.
apply le_mono_right.
firstorder.
Qed.
Theorem T064a: Problem064aTrue. cbv.
apply le_mono_left.
firstorder.
Abort All.
Theorem T064a: Problem064aFalse. cbv.
firstorder.
Abort All.
Theorem T065a: Problem065aTrue. cbv.
firstorder.
Abort All.
Theorem T065a: Problem065aFalse. cbv.
firstorder.
Abort All.
Theorem T066a: Problem066aTrue. cbv.
firstorder.
Qed.
Theorem T067a: Problem067aTrue. cbv.
firstorder.
Qed.
Theorem T068a: Problem068aTrue. cbv.
firstorder.
Qed.
Theorem T069a: Problem069aFalse. cbv. firstorder. Abort All.
Theorem T069a: Problem069aTrue. cbv.
destruct major_A as [major] eqn:majorEq.
intro right.
intro isRight.
intro resident.
intro isResidentIn.
Abort All. (* Problem is broken *)
Theorem T070a: Problem070aFalse. cbv.
destruct on_time_Adv as [onTime].
destruct scandinavian_A as [scandinavian].
firstorder.
Qed. (* Note: I don't understand how this could be proven in FraCoq without scandinavian_A subsective *)
Theorem T071a: Problem071aTrue. cbv.
destruct on_time_Adv as [onTime].
firstorder.
Abort All.
Theorem T071a: Problem071aFalse. cbv.
destruct on_time_Adv as [onTime].
firstorder.
Abort All.
Theorem T072a: Problem072aTrue. cbv.
firstorder.
generalize H0.
apply le_mono_right.
firstorder.
Abort All.
Theorem T072a: Problem072aFalse. cbv.
firstorder.
Abort All.
Theorem T073a: Problem073aTrue. cbv.
destruct major_A as [major] eqn:majorEq.
destruct national_A as [national].
firstorder.
generalize H.
apply le_mono_right.
firstorder.
Abort All.
Theorem T073a: Problem073aFalse. cbv.
(* firstorder. *)
Abort All.
Theorem T074a: Problem074aTrue. cbv.
firstorder.
Abort All.
Theorem T074a: Problem074aFalse. cbv.
firstorder.
Abort All.
Theorem T075a: Problem075aTrue. cbv.
firstorder.
generalize H.
apply le_mono_right.
firstorder.
Abort All.
Theorem T075a: Problem075aFalse. cbv.
firstorder.
Abort All.
Theorem T076a: Problem076aTrue. cbv.
firstorder.
generalize H.
apply le_mono_left.
firstorder.
Qed.
Theorem T079a: Problem079aTrue. cbv.
destruct at_home_Adv as [atHome atHomeVerid].
firstorder.
exists x.
firstorder.
Abort All.
Theorem T079a: Problem079aFalse. cbv.
firstorder.
Abort All.
Theorem T080a: Problem080aTrue. cbv.
destruct at_home_Adv as [atHome atHomeVerid].
firstorder.
generalize H.
apply le_mono_left.
firstorder.
Qed.