Nuprl Lemma : mFOL-sequent-abstract_wf
∀[s:mFOL-sequent()]. (mFOL-sequent-abstract(s) ∈ AbstractFOFormula(mFOL-sequent-freevars(s)))
Proof
Definitions occuring in Statement : 
mFOL-sequent-abstract: mFOL-sequent-abstract(s)
, 
mFOL-sequent-freevars: mFOL-sequent-freevars(s)
, 
mFOL-sequent: mFOL-sequent()
, 
AbstractFOFormula: AbstractFOFormula(vs)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
mFOL-sequent: mFOL-sequent()
, 
mFOL-sequent-abstract: mFOL-sequent-abstract(s)
, 
AbstractFOFormula: AbstractFOFormula(vs)
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
all: ∀x:A. B[x]
Lemmas referenced : 
tuple-type_wf, 
mFOL-hyps-meaning_wf, 
FOSatWith_wf, 
mFOL-freevars_wf, 
subtype_rel_FOAssignment, 
mFOL-sequent-freevars_wf, 
list_wf, 
mFOL_wf, 
mFOL-sequent-freevars-subset-1, 
mFOL-abstract_wf, 
FOAssignment_wf, 
FOStruct_wf, 
mFOL-sequent_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
cut, 
sqequalHypSubstitution, 
productElimination, 
thin, 
sqequalRule, 
lambdaEquality, 
functionEquality, 
lemma_by_obid, 
isectElimination, 
hypothesisEquality, 
hypothesis, 
applyEquality, 
independent_pairEquality, 
productEquality, 
independent_isectElimination, 
dependent_functionElimination, 
because_Cache, 
universeEquality
Latex:
\mforall{}[s:mFOL-sequent()].  (mFOL-sequent-abstract(s)  \mmember{}  AbstractFOFormula(mFOL-sequent-freevars(s)))
Date html generated:
2016_05_15-PM-10_26_58
Last ObjectModification:
2015_12_27-PM-06_26_19
Theory : minimal-first-order-logic
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