Nuprl Lemma : almost_full_wf
∀[T:Type]. ∀[n:ℕ]. ∀[R:n-aryRel(T)]. (almost_full(T;n;R) ∈ ℙ)
Proof
Definitions occuring in Statement :
almost_full: almost_full(T;n;R),
nary-rel: n-aryRel(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
almost_full: almost_full(T;n;R),
so_lambda: λ2x.t[x],
nat: ℕ,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
nary-rel: n-aryRel(T)
Lemmas referenced :
all_wf,
nat_wf,
exists_wf,
int_seg_wf,
strictly-increasing-seq_wf,
subtype_rel_dep_function,
compose_wf,
nary-rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
cumulativity,
hypothesisEquality,
lambdaEquality,
natural_numberEquality,
setElimination,
rename,
because_Cache,
productEquality,
applyEquality,
intEquality,
independent_isectElimination,
lambdaFormation,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[R:n-aryRel(T)]. (almost\_full(T;n;R) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-04_08_11
Last ObjectModification:
2015_12_26-PM-07_54_57
Theory : fan-theorem
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