Nuprl Lemma : diff_functionality_wrt_permr
∀s:DSet. ∀as,as',bs,bs':|s| List. ((as ≡(|s|) as') ⇒ (bs ≡(|s|) bs') ⇒ ((as - bs) ≡(|s|) (as' - bs')))
Proof
Definitions occuring in Statement :
diff: as - bs,
permr: as ≡(T) bs,
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
guard: {T},
rev_implies: P ⇐ Q,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a
Lemmas referenced :
permr_wf,
set_car_wf,
list_wf,
dset_wf,
permr_iff_eq_counts_a,
diff_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
count_diff,
subtype_rel_self,
ndiff_wf,
istype-int,
count_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
inhabitedIsType,
productElimination,
independent_functionElimination,
because_Cache,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
intEquality,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination
Latex:
\mforall{}s:DSet. \mforall{}as,as',bs,bs':|s| List.
((as \mequiv{}(|s|) as') {}\mRightarrow{} (bs \mequiv{}(|s|) bs') {}\mRightarrow{} ((as - bs) \mequiv{}(|s|) (as' - bs')))
Date html generated:
2019_10_16-PM-01_04_23
Last ObjectModification:
2018_10_08-AM-11_16_18
Theory : list_2
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