Nuprl Lemma : FormFvs_wf
∀[c:Type]. ∀[f:Form(c)]. (FormFvs(f) ∈ Atom List)
Proof
Definitions occuring in Statement :
FormFvs: FormFvs(f),
Form: Form(C),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
FormFvs: FormFvs(f),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
all: ∀x:A. B[x],
prop: ℙ,
so_apply: x[s1;s2;s3],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
Form_ind_wf_simple,
top_wf,
list_wf,
subtype_rel_Form,
cons_wf,
nil_wf,
filter_wf5,
l_member_wf,
bnot_wf,
eq_atom_wf,
Form_wf,
l-union_wf,
atom-deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
atomEquality,
hypothesisEquality,
applyEquality,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
lambdaFormation,
setElimination,
rename,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality
Latex:
\mforall{}[c:Type]. \mforall{}[f:Form(c)]. (FormFvs(f) \mmember{} Atom List)
Date html generated:
2018_05_21-PM-11_27_05
Last ObjectModification:
2017_10_11-AM-11_28_46
Theory : PZF
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