Nuprl Lemma : l_before_transitivity
∀[T:Type]. ∀l:T List. ∀x,y,z:T. x before y ∈ l ⇒ y before z ∈ l ⇒ x before z ∈ l supposing no_repeats(T;l)
Proof
Definitions occuring in Statement :
l_before: x before y ∈ l,
no_repeats: no_repeats(T;l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
l_before: x before y ∈ l,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
guard: {T},
or: P ∨ Q,
cand: A c∧ B,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3]
Lemmas referenced :
no_repeats_witness,
sublist_wf,
cons_wf,
nil_wf,
no_repeats_wf,
list_wf,
sublist_transitivity,
cons_sublist_cons,
sublist_weakening,
append_overlapping_sublists,
list_ind_cons_lemma,
istype-void,
list_ind_nil_lemma
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
rename,
Error :universeIsType,
Error :inhabitedIsType,
universeEquality,
dependent_functionElimination,
productElimination,
Error :inrFormation_alt,
because_Cache,
independent_isectElimination,
Error :productIsType,
Error :equalityIsType1,
Error :inlFormation_alt,
independent_pairFormation,
Error :isect_memberEquality_alt,
voidElimination
Latex:
\mforall{}[T:Type]
\mforall{}l:T List. \mforall{}x,y,z:T. x before y \mmember{} l {}\mRightarrow{} y before z \mmember{} l {}\mRightarrow{} x before z \mmember{} l supposing no\_repeats(T;l)
Date html generated:
2019_06_20-PM-01_24_05
Last ObjectModification:
2018_09_29-PM-00_02_53
Theory : list_1
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