Nuprl Lemma : FOSatWith+_wf
∀[vs:ℤ List]. ∀[Dom:Type]. ∀[S:FOStruct+{i:l}(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+{i:l}(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+\{i:l\}(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_16
Last ObjectModification:
2015_12_27-PM-06_33_52
Theory : minimal-first-order-logic
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