Nuprl Lemma : almost-full_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. (AFx,y:T.R[x;y] ∈ ℙ)
Proof
Definitions occuring in Statement :
almost-full: AFx,y:T.R[x; y],
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
almost-full: AFx,y:T.R[x; y],
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s1;s2],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
all_wf,
nat_wf,
squash_wf,
exists_wf,
and_wf,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
hypothesisEquality,
lambdaEquality,
setElimination,
rename,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (AFx,y:T.R[x;y] \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-03_50_53
Last ObjectModification:
2015_12_26-AM-10_17_23
Theory : bar-induction
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