Nuprl Lemma : mFOL-hyps-meaning_wf
∀[concl:mFOL()]. ∀[hyps:mFOL() List]. ∀[Dom:Type]. ∀[S:FOStruct(Dom)]. ∀[a:FOAssignment(mFOL-sequent-freevars(<hyps
                                                                                                              , concl
                                                                                                              >),Dom)].
  (mFOL-hyps-meaning(Dom;S;a;hyps) ∈ Type List)
Proof
Definitions occuring in Statement : 
mFOL-hyps-meaning: mFOL-hyps-meaning(Dom;S;a;hyps)
, 
mFOL-sequent-freevars: mFOL-sequent-freevars(s)
, 
mFOL: mFOL()
, 
FOStruct: FOStruct(Dom)
, 
FOAssignment: FOAssignment(vs,Dom)
, 
list: T List
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
pair: <a, b>
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
mFOL-hyps-meaning: mFOL-hyps-meaning(Dom;S;a;hyps)
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
mFOL-sequent: mFOL-sequent()
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
implies: P 
⇒ Q
Lemmas referenced : 
list-subtype, 
mFOL_wf, 
map_wf, 
l_member_wf, 
FOSatWith_wf, 
mFOL-freevars_wf, 
subtype_rel_FOAssignment, 
mFOL-sequent-freevars_wf, 
subtype_rel_product, 
list_wf, 
subtype_rel_list, 
subtype_rel_self, 
mFOL-sequent-freevars-subset-2, 
mFOL-abstract_wf, 
FOAssignment_wf, 
FOStruct_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesis, 
hypothesisEquality, 
equalityTransitivity, 
equalitySymmetry, 
sqequalRule, 
instantiate, 
setEquality, 
applyEquality, 
lambdaEquality, 
cumulativity, 
universeEquality, 
because_Cache, 
lambdaFormation, 
setElimination, 
rename, 
independent_pairEquality, 
independent_isectElimination, 
dependent_functionElimination, 
independent_functionElimination, 
axiomEquality, 
productEquality, 
isect_memberEquality
Latex:
\mforall{}[concl:mFOL()].  \mforall{}[hyps:mFOL()  List].  \mforall{}[Dom:Type].  \mforall{}[S:FOStruct(Dom)].
\mforall{}[a:FOAssignment(mFOL-sequent-freevars(<hyps,  concl>),Dom)].
    (mFOL-hyps-meaning(Dom;S;a;hyps)  \mmember{}  Type  List)
Date html generated:
2016_05_15-PM-10_26_38
Last ObjectModification:
2015_12_27-PM-06_26_49
Theory : minimal-first-order-logic
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