Nuprl Lemma : FormSafe1'_wf
∀[C:Type]. ∀[f:Form(C)]. (FormSafe1'(f) ∈ (Atom List) ⟶ ℙ)
Proof
Definitions occuring in Statement :
FormSafe1': FormSafe1'(f),
Form: Form(C),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
FormSafe1': FormSafe1'(f),
subtype_rel: A ⊆r B,
prop: ℙ,
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]),
so_apply: x[s1;s2;s3],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
and: P ∧ Q,
or: P ∨ Q,
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,
false_wf,
Form_wf,
or_wf,
assert_wf,
null_wf3,
subtype_rel_list,
exists_wf,
set-equal_wf,
cons_wf,
nil_wf,
FormVar?_wf,
equal-wf-T-base,
FormVar-name_wf,
atom_subtype_base,
not_wf,
l_member_wf,
FormFvs_wf,
l_subset_wf,
list-diff_wf,
atom-deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
applyEquality,
lambdaEquality,
cumulativity,
hypothesisEquality,
universeEquality,
functionEquality,
atomEquality,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
productEquality,
functionExtensionality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[C:Type]. \mforall{}[f:Form(C)]. (FormSafe1'(f) \mmember{} (Atom List) {}\mrightarrow{} \mBbbP{})
Date html generated:
2018_05_21-PM-11_29_08
Last ObjectModification:
2017_10_12-AM-00_15_40
Theory : PZF
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