Nuprl Lemma : mFO-dest-quantifier_wf
∀[T:Type]. ∀[F:ℤ ⟶ mFOL() ⟶ (T?)]. ∀[fmla:mFOL()]. ∀[isall:𝔹].
(let v,b = dest-if isall then all else exists(fmla); in
F[v;b] ∈ T?)
Proof
Definitions occuring in Statement :
mFO-dest-quantifier: mFO-dest-quantifier,
mFOL: mFOL(),
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mFO-dest-quantifier: mFO-dest-quantifier,
all: ∀x:A. B[x],
implies: P ⇒ Q,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
so_apply: x[s1;s2],
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Lemmas referenced :
mFOquant?_wf,
eqtt_to_assert,
ifthenelse_wf,
eq_bool_wf,
mFOquant-isall_wf,
unit_wf2,
mFOquant-var_wf,
mFOquant-body_wf,
it_wf,
eqff_to_assert,
equal_wf,
bool_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
mFOL_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
sqequalRule,
unionEquality,
cumulativity,
applyEquality,
functionExtensionality,
intEquality,
inrEquality,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
independent_functionElimination,
voidElimination,
axiomEquality,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[F:\mBbbZ{} {}\mrightarrow{} mFOL() {}\mrightarrow{} (T?)]. \mforall{}[fmla:mFOL()]. \mforall{}[isall:\mBbbB{}].
(let v,b = dest-if isall then all else exists(fmla); in
F[v;b] \mmember{} T?)
Date html generated:
2018_05_21-PM-10_21_47
Last ObjectModification:
2017_07_26-PM-06_38_01
Theory : minimal-first-order-logic
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