Nuprl Lemma : mFOquant_wf
∀[isall:𝔹]. ∀[var:ℤ]. ∀[body:mFOL()]. (mFOquant(isall;var;body) ∈ mFOL())
Proof
Definitions occuring in Statement :
mFOquant: mFOquant(isall;var;body),
mFOL: mFOL(),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mFOL: mFOL(),
mFOquant: mFOquant(isall;var;body),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
subtype_rel: A ⊆r B,
ext-eq: A ≡ B,
and: P ∧ Q,
mFOLco_size: mFOLco_size(p),
mFOL_size: mFOL_size(p),
spreadn: spread3,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
mFOLco-ext,
mFOLco_wf,
ifthenelse_wf,
eq_atom_wf,
list_wf,
bool_wf,
add_nat_wf,
false_wf,
le_wf,
mFOL_size_wf,
nat_wf,
value-type-has-value,
set-value-type,
int-value-type,
equal_wf,
has-value_wf-partial,
mFOLco_size_wf,
mFOL_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
dependent_set_memberEquality,
introduction,
extract_by_obid,
hypothesis,
sqequalRule,
dependent_pairEquality,
tokenEquality,
hypothesisEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productEquality,
intEquality,
instantiate,
isectElimination,
universeEquality,
atomEquality,
voidEquality,
applyEquality,
productElimination,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
independent_isectElimination,
lambdaEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
because_Cache
Latex:
\mforall{}[isall:\mBbbB{}]. \mforall{}[var:\mBbbZ{}]. \mforall{}[body:mFOL()]. (mFOquant(isall;var;body) \mmember{} mFOL())
Date html generated:
2018_05_21-PM-10_20_58
Last ObjectModification:
2017_07_26-PM-06_37_41
Theory : minimal-first-order-logic
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