Nuprl Lemma : implies-bfs-equiv
∀[K:RngSig]. ∀[S:Type]. ∀as,bs:basic-formal-sum(K;S). (bfs-reduce(K;S;as;bs) ⇒ bfs-equiv(K;S;as;bs))
Proof
Definitions occuring in Statement :
bfs-equiv: bfs-equiv(K;S;fs1;fs2),
bfs-reduce: bfs-reduce(K;S;as;bs),
basic-formal-sum: basic-formal-sum(K;S),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type,
rng_sig: RngSig
Definitions unfolded in proof :
guard: {T},
prop: ℙ,
bfs-equiv: bfs-equiv(K;S;fs1;fs2),
infix_ap: x f y,
rel_implies: R1 => R2,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x]
Lemmas referenced :
rng_sig_wf,
basic-formal-sum_wf,
bfs-reduce_wf,
implies-least-equiv
Rules used in proof :
universeEquality,
sqequalRule,
hypothesis,
cumulativity,
hypothesisEquality,
lambdaEquality,
because_Cache,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[K:RngSig]. \mforall{}[S:Type].
\mforall{}as,bs:basic-formal-sum(K;S). (bfs-reduce(K;S;as;bs) {}\mRightarrow{} bfs-equiv(K;S;as;bs))
Date html generated:
2018_05_22-PM-09_45_12
Last ObjectModification:
2018_01_09-AM-11_07_09
Theory : linear!algebra
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