Nuprl Lemma : fseg_transitivity
∀[T:Type]. ∀l1,l2,l3:T List. (fseg(T;l1;l2) ⇒ fseg(T;l2;l3) ⇒ fseg(T;l1;l3))
Proof
Definitions occuring in Statement :
fseg: fseg(T;L1;L2),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
fseg: fseg(T;L1;L2),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top
Lemmas referenced :
length_wf_nat,
equal_wf,
nat_wf,
exists_wf,
list_wf,
append_wf,
append_assoc
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
dependent_set_memberEquality,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
because_Cache,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
lambdaEquality,
setElimination,
rename,
universeEquality,
dependent_pairFormation,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity
Latex:
\mforall{}[T:Type]. \mforall{}l1,l2,l3:T List. (fseg(T;l1;l2) {}\mRightarrow{} fseg(T;l2;l3) {}\mRightarrow{} fseg(T;l1;l3))
Date html generated:
2016_10_25-AM-10_45_16
Last ObjectModification:
2016_07_12-AM-06_55_02
Theory : general
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