Nuprl Lemma : FOL-hyps-meaning_wf
∀[concl:mFOL()]. ∀[hyps:mFOL() List]. ∀[Dom:Type]. ∀[S:FOStruct+{i:l}(Dom)].
∀[a:FOAssignment(mFOL-sequent-freevars(<hyps, concl>),Dom)].
(FOL-hyps-meaning(Dom;S;a;hyps) ∈ Type List)
Proof
Definitions occuring in Statement :
FOL-hyps-meaning: FOL-hyps-meaning(Dom;S;a;hyps),
mFOL-sequent-freevars: mFOL-sequent-freevars(s),
mFOL: mFOL(),
FOStruct+: FOStruct+{i:l}(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,
FOL-hyps-meaning: FOL-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,
FOL-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+\{i:l\}(Dom)].
\mforall{}[a:FOAssignment(mFOL-sequent-freevars(<hyps, concl>),Dom)].
(FOL-hyps-meaning(Dom;S;a;hyps) \mmember{} Type List)
Date html generated:
2016_05_15-PM-10_26_48
Last ObjectModification:
2015_12_27-PM-06_26_45
Theory : minimal-first-order-logic
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