Nuprl Lemma : cons_interleaving2
∀[T:Type]. ∀x:T. ∀L,L1,L2:T List. (interleaving(T;L1;L2;L) ⇒ interleaving(T;L1;[x / L2];[x / L]))
Proof
Definitions occuring in Statement :
interleaving: interleaving(T;L1;L2;L),
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
cons_wf,
interleaving_symmetry,
cons_interleaving,
interleaving_wf,
list_wf
Rules used in proof :
because_Cache,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
productElimination,
independent_functionElimination,
isect_memberFormation_alt,
lambdaFormation,
universeIsType,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}x:T. \mforall{}L,L1,L2:T List. (interleaving(T;L1;L2;L) {}\mRightarrow{} interleaving(T;L1;[x / L2];[x / L]))
Date html generated:
2019_10_15-AM-10_55_40
Last ObjectModification:
2018_09_27-AM-10_43_21
Theory : list!
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