Nuprl Lemma : cons-ndlist
∀[T:Type]. ∀[L:ndlist(T)]. ∀[x:T]. [x / L] ∈ ndlist(T) supposing ¬(x ∈ L)
Proof
Definitions occuring in Statement :
ndlist: ndlist(T),
l_member: (x ∈ l),
cons: [a / b],
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
ndlist: ndlist(T),
uiff: uiff(P;Q),
and: P ∧ Q,
cand: A c∧ B,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T
Lemmas referenced :
sq_stable__no_repeats,
no_repeats_wf,
no_repeats_cons,
cons_wf,
ndlist_wf,
l_member_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
isect_memberEquality,
because_Cache,
universeEquality,
dependent_set_memberEquality,
productElimination,
independent_isectElimination,
independent_pairFormation,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}[T:Type]. \mforall{}[L:ndlist(T)]. \mforall{}[x:T]. [x / L] \mmember{} ndlist(T) supposing \mneg{}(x \mmember{} L)
Date html generated:
2016_05_14-PM-03_31_09
Last ObjectModification:
2016_01_14-PM-11_20_29
Theory : decidable!equality
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