Nuprl Lemma : church-inductive_wf
∀[x:cNat]. (church-inductive{i:l}(x) ∈ ℙ')
Proof
Definitions occuring in Statement :
church-inductive: church-inductive{i:l}(x),
church-Nat: cNat,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
church-inductive: church-inductive{i:l}(x),
prop: ℙ,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x]
Lemmas referenced :
church-Nat_wf,
church-zero_wf,
subtype_rel_self,
church-succ_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
isectEquality,
functionEquality,
extract_by_obid,
hypothesis,
universeEquality,
cumulativity,
applyEquality,
hypothesisEquality,
thin,
instantiate,
sqequalHypSubstitution,
isectElimination,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType
Latex:
\mforall{}[x:cNat]. (church-inductive\{i:l\}(x) \mmember{} \mBbbP{}')
Date html generated:
2020_05_20-AM-08_05_32
Last ObjectModification:
2019_11_15-PM-10_11_45
Theory : general
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