Nuprl Lemma : comb_for_firstn_wf
λA,as,n,z. firstn(n;as) ∈ A:Type ⟶ as:(A List) ⟶ n:ℤ ⟶ (↓True) ⟶ (A List)
Proof
Definitions occuring in Statement :
firstn: firstn(n;as),
list: T List,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
firstn_wf,
squash_wf,
true_wf,
istype-int,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
Error :universeIsType,
universeEquality
Latex:
\mlambda{}A,as,n,z. firstn(n;as) \mmember{} A:Type {}\mrightarrow{} as:(A List) {}\mrightarrow{} n:\mBbbZ{} {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} (A List)
Date html generated:
2019_06_20-PM-00_43_10
Last ObjectModification:
2018_10_01-PM-00_27_54
Theory : list_0
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