Nuprl Lemma : comb_for_hd_wf_listp
λA,l,z. hd(l) ∈ A:Type ⟶ l:A List+ ⟶ (↓True) ⟶ A
Proof
Definitions occuring in Statement :
listp: A List+,
hd: hd(l),
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 :
hd_wf_listp,
squash_wf,
true_wf,
listp_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,l,z. hd(l) \mmember{} A:Type {}\mrightarrow{} l:A List\msupplus{} {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} A
Date html generated:
2019_06_20-PM-01_27_51
Last ObjectModification:
2018_10_05-AM-09_40_48
Theory : list_1
Home
Index