Nuprl Lemma : K-sat_wf
∀[K:mKripkeStruct]. ∀[i:World]. ∀[fmla:mFOL()]. ∀[a:FOAssignment(mFOL-freevars(fmla),Dom(i))]. (i,a |= fmla ∈ ℙ)
Proof
Definitions occuring in Statement :
K-sat: i,a |= fmla,
K-dom: Dom(i),
K-world: World,
mFO-Kripke-struct: mKripkeStruct,
mFOL-freevars: mFOL-freevars(fmla),
mFOL: mFOL(),
FOAssignment: FOAssignment(vs,Dom),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
K-sat: i,a |= fmla
Lemmas referenced :
FOSatWith_wf,
mFOL-freevars_wf,
K-dom_wf,
K-struct_wf,
mFOL-abstract_wf,
FOAssignment_wf,
mFOL_wf,
K-world_wf,
mFO-Kripke-struct_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[K:mKripkeStruct]. \mforall{}[i:World]. \mforall{}[fmla:mFOL()]. \mforall{}[a:FOAssignment(mFOL-freevars(fmla),Dom(i))].
(i,a |= fmla \mmember{} \mBbbP{})
Date html generated:
2019_10_16-AM-11_44_58
Last ObjectModification:
2018_10_12-PM-10_19_41
Theory : minimal-first-order-logic
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