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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