Nuprl Lemma : PZF_safe_functionality_subset
∀[C:Type]. ∀[phi:Form(C)]. ∀[vs,ws:Atom List].
(↑PZF_safe(phi;vs)) ⇒ (↑PZF_safe(phi;ws)) supposing l_subset(Atom;ws;vs)
Proof
Definitions occuring in Statement :
PZF_safe: PZF_safe(phi;vs),
Form: Form(C),
l_subset: l_subset(T;as;bs),
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
all: ∀x:A. B[x],
guard: {T},
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
PZF-safe: PZF-safe(phi;vs)
Lemmas referenced :
FormSafe1_functionality,
assert_wf,
PZF_safe_wf,
assert_witness,
l_subset_wf,
list_wf,
Form_wf,
assert-PZF_safe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
isectElimination,
cumulativity,
sqequalRule,
lambdaEquality,
atomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
productElimination
Latex:
\mforall{}[C:Type]. \mforall{}[phi:Form(C)]. \mforall{}[vs,ws:Atom List].
(\muparrow{}PZF\_safe(phi;vs)) {}\mRightarrow{} (\muparrow{}PZF\_safe(phi;ws)) supposing l\_subset(Atom;ws;vs)
Date html generated:
2018_05_21-PM-11_35_57
Last ObjectModification:
2017_10_12-PM-04_23_19
Theory : PZF
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