Nuprl Lemma : FormNot-body_wf
∀[C:Type]. ∀[v:Form(C)]. FormNot-body(v) ∈ Form(C) supposing ↑FormNot?(v)
Proof
Definitions occuring in Statement :
FormNot-body: FormNot-body(v)
,
FormNot?: FormNot?(v)
,
Form: Form(C)
,
assert: ↑b
,
uimplies: b supposing a
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
uimplies: b supposing a
,
member: t ∈ T
,
ext-eq: A ≡ B
,
and: P ∧ Q
,
subtype_rel: A ⊆r B
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
bool: 𝔹
,
unit: Unit
,
it: ⋅
,
btrue: tt
,
uiff: uiff(P;Q)
,
sq_type: SQType(T)
,
guard: {T}
,
eq_atom: x =a y
,
ifthenelse: if b then t else f fi
,
FormNot?: FormNot?(v)
,
pi1: fst(t)
,
assert: ↑b
,
bfalse: ff
,
false: False
,
exists: ∃x:A. B[x]
,
prop: ℙ
,
or: P ∨ Q
,
bnot: ¬bb
,
FormNot-body: FormNot-body(v)
,
pi2: snd(t)
Lemmas referenced :
Form-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
assert_wf,
FormNot?_wf,
Form_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
promote_hyp,
productElimination,
hypothesis_subsumption,
hypothesis,
applyEquality,
sqequalRule,
tokenEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
instantiate,
cumulativity,
atomEquality,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
voidElimination,
dependent_pairFormation,
universeEquality
Latex:
\mforall{}[C:Type]. \mforall{}[v:Form(C)]. FormNot-body(v) \mmember{} Form(C) supposing \muparrow{}FormNot?(v)
Date html generated:
2018_05_21-PM-11_24_36
Last ObjectModification:
2017_10_13-PM-07_01_22
Theory : PZF
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