Nuprl Lemma : l_all_since_wf
∀[T:Type]. ∀[P:T ⟶ ℙ]. ∀[L:T List]. ∀[a:T]. ((∀x≥a∈L.P[x]) ∈ ℙ)
Proof
Definitions occuring in Statement :
l_all_since: (∀x≥a∈L.P[x]),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
l_all_since: (∀x≥a∈L.P[x]),
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
subtype_rel_self,
all_wf,
l_before_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
applyEquality,
hypothesisEquality,
hypothesis,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
universeEquality,
lambdaEquality,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality,
because_Cache,
functionIsType,
cumulativity
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[L:T List]. \mforall{}[a:T]. ((\mforall{}x\mgeq{}a\mmember{}L.P[x]) \mmember{} \mBbbP{})
Date html generated:
2019_10_15-AM-10_54_37
Last ObjectModification:
2018_09_27-AM-09_38_58
Theory : list!
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