Nuprl Lemma : safety_induced
∀[A,B:Type]. ∀f:A ⟶ B. ∀[P:(B List) ⟶ ℙ]. (safety(B;L.P[L]) ⇒ safety(A;L.P[map(f;L)]))
Proof
Definitions occuring in Statement :
safety: safety(A;tr.P[tr]),
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
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],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x]
Lemmas referenced :
map_wf,
iseg_wf,
list_wf,
all_wf,
iseg_map
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
lambdaFormation,
cut,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
independent_functionElimination,
applyEquality,
lambdaEquality,
functionEquality,
functionIsType,
universeIsType,
universeEquality,
inhabitedIsType
Latex:
\mforall{}[A,B:Type]. \mforall{}f:A {}\mrightarrow{} B. \mforall{}[P:(B List) {}\mrightarrow{} \mBbbP{}]. (safety(B;L.P[L]) {}\mRightarrow{} safety(A;L.P[map(f;L)]))
Date html generated:
2019_10_15-AM-10_58_25
Last ObjectModification:
2018_09_27-AM-09_47_02
Theory : list!
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