Nuprl Lemma : tcWO_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. (tcWO(T;x,y.R[x;y]) ∈ ℙ)
Proof
Definitions occuring in Statement :
tcWO: tcWO(T;x,y.>[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,
tcWO: tcWO(T;x,y.>[x; y]),
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
so_apply: x[s],
all: ∀x:A. B[x],
nat: ℕ,
exists: ∃x:A. B[x]
Lemmas referenced :
all_wf,
nat_wf,
squash_wf,
exists_wf,
less_than_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
because_Cache,
functionEquality,
applyEquality,
hypothesis,
universeEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (tcWO(T;x,y.R[x;y]) \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-03_51_50
Last ObjectModification:
2015_12_26-AM-10_17_22
Theory : bar-induction
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