Nuprl Lemma : lmin_com
∀s:DSet. ∀as,bs:|s| List. (lmin(s;as;bs) ≡(|s|) lmin(s;bs;as))
Proof
Definitions occuring in Statement :
lmin: lmin(s;as;bs),
permr: as ≡(T) bs,
list: T List,
all: ∀x:A. B[x],
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
dset: DSet,
true: True,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T}
Lemmas referenced :
permr_iff_eq_counts,
lmin_wf,
set_car_wf,
list_wf,
dset_wf,
imin_com,
count_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
count_lmin,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
universeIsType,
isectElimination,
setElimination,
rename,
inhabitedIsType,
intEquality,
natural_numberEquality,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination
Latex:
\mforall{}s:DSet. \mforall{}as,bs:|s| List. (lmin(s;as;bs) \mequiv{}(|s|) lmin(s;bs;as))
Date html generated:
2019_10_16-PM-01_04_35
Last ObjectModification:
2018_10_08-AM-10_22_37
Theory : list_2
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