Nuprl Lemma : FOSatWith_wf
∀[vs:ℤ List]. ∀[Dom:Type]. ∀[S:FOStruct(Dom)]. ∀[a:FOAssignment(vs,Dom)]. ∀[fmla:AbstractFOFormula(vs)].
(Dom,S,a |= fmla ∈ ℙ)
Proof
Definitions occuring in Statement :
FOSatWith: Dom,S,a |= fmla,
AbstractFOFormula: AbstractFOFormula(vs),
FOStruct: FOStruct(Dom),
FOAssignment: FOAssignment(vs,Dom),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
FOSatWith: Dom,S,a |= fmla,
AbstractFOFormula: AbstractFOFormula(vs)
Lemmas referenced :
AbstractFOFormula_wf,
FOAssignment_wf,
FOStruct_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
sqequalHypSubstitution,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
isect_memberEquality,
because_Cache,
universeEquality,
intEquality
Latex:
\mforall{}[vs:\mBbbZ{} List]. \mforall{}[Dom:Type]. \mforall{}[S:FOStruct(Dom)]. \mforall{}[a:FOAssignment(vs,Dom)].
\mforall{}[fmla:AbstractFOFormula(vs)].
(Dom,S,a |= fmla \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-10_12_14
Last ObjectModification:
2015_12_27-PM-06_33_51
Theory : minimal-first-order-logic
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