Nuprl Lemma : int_upper_subtype_nat
∀[n:ℕ]. ({n...} ⊆r ℕ)
Proof
Definitions occuring in Statement :
int_upper: {i...},
nat: ℕ,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_upper: {i...},
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
le: A ≤ B,
and: P ∧ Q,
sq_stable: SqStable(P),
guard: {T},
squash: ↓T
Lemmas referenced :
nat_wf,
le_transitivity,
decidable__le,
sq_stable_from_decidable,
le_wf,
subtype_rel_sets
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
because_Cache,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
independent_isectElimination,
setEquality,
lambdaFormation,
productElimination,
independent_functionElimination,
dependent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
axiomEquality
Latex:
\mforall{}[n:\mBbbN{}]. (\{n...\} \msubseteq{}r \mBbbN{})
Date html generated:
2016_05_13-PM-03_33_00
Last ObjectModification:
2016_01_14-PM-06_40_56
Theory : arithmetic
Home
Index