Nuprl Lemma : u-almost-full_wf
∀[A:ℕ ⟶ ℙ]. (u-almost-full(n.A[n]) ∈ ℙ)
Proof
Definitions occuring in Statement :
u-almost-full: u-almost-full(n.A[n]),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
u-almost-full: u-almost-full(n.A[n]),
so_lambda: λ2x.t[x],
so_apply: x[s],
strict-inc: StrictInc,
exists: ∃x:A. B[x],
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
all_wf,
strict-inc_wf,
quotient_wf,
exists_wf,
nat_wf,
true_wf,
equiv_rel_true
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
applyEquality,
hypothesisEquality,
setElimination,
rename,
because_Cache,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A:\mBbbN{} {}\mrightarrow{} \mBbbP{}]. (u-almost-full(n.A[n]) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-09_48_51
Last ObjectModification:
2015_12_26-PM-09_46_58
Theory : continuity
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