Nuprl Lemma : all_safety
∀[T,I:Type]. ∀[P:I ⟶ (T List) ⟶ ℙ]. ((∀x:I. safety(T;L.P[x;L])) ⇒ safety(T;L.∀x:I. P[x;L]))
Proof
Definitions occuring in Statement :
safety: safety(A;tr.P[tr]),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
safety: safety(A;tr.P[tr]),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
so_apply: x[s],
guard: {T}
Lemmas referenced :
all_wf,
iseg_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
lambdaFormation,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
applyEquality,
hypothesis,
functionEquality,
functionIsType,
universeIsType,
universeEquality,
inhabitedIsType,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[T,I:Type]. \mforall{}[P:I {}\mrightarrow{} (T List) {}\mrightarrow{} \mBbbP{}]. ((\mforall{}x:I. safety(T;L.P[x;L])) {}\mRightarrow{} safety(T;L.\mforall{}x:I. P[x;L]))
Date html generated:
2019_10_15-AM-10_54_08
Last ObjectModification:
2018_09_27-AM-10_02_42
Theory : list!
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