Nuprl Lemma : strong_safety_safety
∀[A:Type]. ∀[P:(A List) ⟶ ℙ]. (strong_safety(A;x.P[x]) ⇒ safety(A;x.P[x]))
Proof
Definitions occuring in Statement :
strong_safety: strong_safety(T;tr.P[tr]),
safety: safety(A;tr.P[tr]),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
safety: safety(A;tr.P[tr]),
strong_safety: strong_safety(T;tr.P[tr]),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
guard: {T},
member: t ∈ T,
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x]
Lemmas referenced :
sublist_iseg,
iseg_wf,
list_wf,
all_wf,
sublist_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
hypothesis,
thin,
sqequalHypSubstitution,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
lemma_by_obid,
isectElimination,
because_Cache,
applyEquality,
lambdaEquality,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[P:(A List) {}\mrightarrow{} \mBbbP{}]. (strong\_safety(A;x.P[x]) {}\mRightarrow{} safety(A;x.P[x]))
Date html generated:
2016_05_15-PM-02_06_30
Last ObjectModification:
2015_12_27-AM-00_21_58
Theory : list!
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