Nuprl Lemma : all_mset_elim
∀s:DSet. ∀F:MSet{s} ⟶ ℙ. ((∀a:MSet{s}. SqStable(F[a])) ⇒ (∀a:MSet{s}. F[a] ⇐⇒ ∀a:|s| List. F[mk_mset(a)]))
Proof
Definitions occuring in Statement :
mk_mset: mk_mset(as),
mset: MSet{s},
list: T List,
sq_stable: SqStable(P),
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
mk_mset: mk_mset(as),
mset: MSet{s},
dset: DSet,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
all_wf,
mset_wf,
sq_stable_wf,
dset_wf,
all_quot_elim,
list_wf,
set_car_wf,
permr_wf,
permr_equiv_rel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
applyEquality,
functionEquality,
cumulativity,
universeEquality,
setElimination,
rename,
independent_functionElimination
Latex:
\mforall{}s:DSet. \mforall{}F:MSet\{s\} {}\mrightarrow{} \mBbbP{}.
((\mforall{}a:MSet\{s\}. SqStable(F[a])) {}\mRightarrow{} (\mforall{}a:MSet\{s\}. F[a] \mLeftarrow{}{}\mRightarrow{} \mforall{}a:|s| List. F[mk\_mset(a)]))
Date html generated:
2016_05_16-AM-07_46_20
Last ObjectModification:
2015_12_28-PM-06_03_59
Theory : mset
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