Nuprl Lemma : church-iS
∀[x:cNat]. (cS ∈ church-inductive{i:l}(x) ⟶ church-inductive{i:l}(cS x))
Proof
Definitions occuring in Statement :
church-inductive: church-inductive{i:l}(x),
church-succ: cS,
church-Nat: cNat,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
church-succ: cS,
church-inductive: church-inductive{i:l}(x),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
church-Nat: cNat,
prop: ℙ
Lemmas referenced :
trivial-equal,
church-Nat_wf,
istype-universe,
church-zero_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
isect_memberFormation_alt,
introduction,
cut,
lambdaEquality_alt,
isect_memberEquality_alt,
lambdaFormation_alt,
applyEquality,
hypothesisEquality,
isectElimination,
equalityTransitivity,
equalitySymmetry,
hypothesis,
inhabitedIsType,
sqequalHypSubstitution,
functionIsType,
universeIsType,
thin,
because_Cache,
instantiate,
extract_by_obid,
isectIsType,
universeEquality,
dependent_functionElimination,
axiomEquality
Latex:
\mforall{}[x:cNat]. (cS \mmember{} church-inductive\{i:l\}(x) {}\mrightarrow{} church-inductive\{i:l\}(cS x))
Date html generated:
2020_05_20-AM-08_05_40
Last ObjectModification:
2019_11_15-PM-10_51_10
Theory : general
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