Nuprl Lemma : nat-partial-nat
∀[n:ℕ]. (n ∈ partial(ℕ))
Proof
Definitions occuring in Statement :
partial: partial(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
inclusion-partial,
nat_wf,
set-value-type,
le_wf,
int-value-type
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
applyEquality,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
independent_isectElimination,
sqequalRule,
intEquality,
lambdaEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}]. (n \mmember{} partial(\mBbbN{}))
Date html generated:
2018_05_21-PM-00_05_10
Last ObjectModification:
2017_10_18-PM-04_26_22
Theory : partial_1
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