Nuprl Lemma : church-iZ
cZ ∈ church-inductive{i:l}(cZ)
Proof
Definitions occuring in Statement :
church-inductive: church-inductive{i:l}(x),
church-zero: cZ,
member: t ∈ T
Definitions unfolded in proof :
church-zero: cZ,
church-inductive: church-inductive{i:l}(x),
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
church-Nat: cNat,
prop: ℙ
Lemmas referenced :
church-Nat_wf,
church-succ_wf,
trivial-equal,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
isect_memberEquality_alt,
lambdaEquality_alt,
hypothesisEquality,
isectIsType,
universeIsType,
cut,
introduction,
extract_by_obid,
hypothesis,
functionIsType,
applyEquality,
thin,
because_Cache,
sqequalHypSubstitution,
instantiate,
isectElimination,
inhabitedIsType,
universeEquality
Latex:
cZ \mmember{} church-inductive\{i:l\}(cZ)
Date html generated:
2020_05_20-AM-08_05_36
Last ObjectModification:
2019_11_15-PM-10_34_14
Theory : general
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