Nuprl Lemma : bfs-reduce-strong-subtype-iff
∀[K:RngSig]. ∀[S,T:Type].
∀[as,bs:basic-formal-sum(K;S)]. (bfs-reduce(K;T;as;bs) ⇐⇒ bfs-reduce(K;S;as;bs)) supposing strong-subtype(S;T)
Proof
Definitions occuring in Statement :
bfs-reduce: bfs-reduce(K;S;as;bs),
basic-formal-sum: basic-formal-sum(K;S),
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
universe: Type,
rng_sig: RngSig
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
subtype_rel: A ⊆r B,
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
prop: ℙ,
rev_implies: P ⇐ Q,
guard: {T}
Lemmas referenced :
strong-subtype_witness,
bfs-reduce-strong-subtype,
bfs-reduce_wf,
basic-formal-sum-subtype,
bfs-reduce-subtype1,
basic-formal-sum_wf,
strong-subtype_wf,
istype-universe,
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
rename,
independent_pairFormation,
lambdaFormation_alt,
independent_isectElimination,
universeIsType,
applyEquality,
productElimination,
sqequalRule,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[K:RngSig]. \mforall{}[S,T:Type].
\mforall{}[as,bs:basic-formal-sum(K;S)]. (bfs-reduce(K;T;as;bs) \mLeftarrow{}{}\mRightarrow{} bfs-reduce(K;S;as;bs))
supposing strong-subtype(S;T)
Date html generated:
2019_10_31-AM-06_29_24
Last ObjectModification:
2019_08_15-PM-04_45_27
Theory : linear!algebra
Home
Index