Nuprl Lemma : comb_for_l_succ_wf
λT,l,x,P,z. y = succ(x) in l⇒ P[y] ∈ T:Type ⟶ l:(T List) ⟶ x:T ⟶ P:(T ⟶ ℙ) ⟶ (↓True) ⟶ ℙ
Proof
Definitions occuring in Statement :
l_succ: l_succ,
list: T List,
prop: ℙ,
so_apply: x[s],
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
l_succ_wf,
squash_wf,
true_wf,
istype-universe,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeIsType,
functionIsType,
inhabitedIsType,
universeEquality
Latex:
\mlambda{}T,l,x,P,z. y = succ(x) in l{}\mRightarrow{} P[y] \mmember{} T:Type {}\mrightarrow{} l:(T List) {}\mrightarrow{} x:T {}\mrightarrow{} P:(T {}\mrightarrow{} \mBbbP{}) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbP{}
Date html generated:
2019_10_15-AM-10_53_16
Last ObjectModification:
2018_10_09-AM-10_31_07
Theory : list!
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