Nuprl Lemma : mFOLisAll_wf
∀[A:mFOL()]. (mFOLisAll(A) ∈ 𝔹)
Proof
Definitions occuring in Statement :
mFOLisAll: mFOLisAll(A),
mFOL: mFOL(),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mFOLisAll: mFOLisAll(A),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff,
prop: ℙ
Lemmas referenced :
mFOquant?_wf,
bool_wf,
eqtt_to_assert,
mFOquant-isall_wf,
equal_wf,
mFOL_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[A:mFOL()]. (mFOLisAll(A) \mmember{} \mBbbB{})
Date html generated:
2018_05_21-PM-10_24_59
Last ObjectModification:
2017_07_26-PM-06_38_45
Theory : minimal-first-order-logic
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