Nuprl Lemma : comb_for_l_member_wf
λT,x,l,z. (x ∈ l) ∈ T:Type ⟶ x:T ⟶ l:(T List) ⟶ (↓True) ⟶ ℙ
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
list: T List,
prop: ℙ,
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_member_wf,
squash_wf,
true_wf,
list_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeIsType,
universeEquality
Latex:
\mlambda{}T,x,l,z. (x \mmember{} l) \mmember{} T:Type {}\mrightarrow{} x:T {}\mrightarrow{} l:(T List) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbP{}
Date html generated:
2019_10_15-AM-10_52_57
Last ObjectModification:
2018_10_09-AM-10_31_09
Theory : list!
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