Nuprl Lemma : FOL-sequent-abstract_wf
∀[s:mFOL-sequent()]. (FOL-sequent-abstract(s) ∈ AbstractFOFormula+(mFOL-sequent-freevars(s)))
Proof
Definitions occuring in Statement :
FOL-sequent-abstract: FOL-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(),
FOL-sequent-abstract: FOL-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,
FOL-hyps-meaning_wf,
FOSatWith+_wf,
mFOL-freevars_wf,
subtype_rel_FOAssignment,
mFOL-sequent-freevars_wf,
list_wf,
mFOL_wf,
mFOL-sequent-freevars-subset-1,
FOL-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()]. (FOL-sequent-abstract(s) \mmember{} AbstractFOFormula+(mFOL-sequent-freevars(s)))
Date html generated:
2016_05_15-PM-10_27_05
Last ObjectModification:
2015_12_27-PM-06_26_08
Theory : minimal-first-order-logic
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