Nuprl Lemma : mFOL-sequent-freevars-subset-1
∀hyps:mFOL() List. ∀concl:mFOL(). mFOL-freevars(concl) ⊆ mFOL-sequent-freevars(<hyps, concl>)
Proof
Definitions occuring in Statement :
mFOL-sequent-freevars: mFOL-sequent-freevars(s),
mFOL-freevars: mFOL-freevars(fmla),
mFOL: mFOL(),
l_contains: A ⊆ B,
list: T List,
all: ∀x:A. B[x],
pair: <a, b>,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
mFOL-sequent: mFOL-sequent(),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
pi2: snd(t),
uimplies: b supposing a
Lemmas referenced :
mFOL-sequent-freevars-contains-concl,
list_wf,
mFOL_wf,
mFOL-freevars_wf,
l_contains_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
independent_pairEquality,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
sqequalRule,
productEquality,
isectElimination,
independent_functionElimination,
intEquality,
because_Cache,
independent_isectElimination
Latex:
\mforall{}hyps:mFOL() List. \mforall{}concl:mFOL(). mFOL-freevars(concl) \msubseteq{} mFOL-sequent-freevars(<hyps, concl>)
Date html generated:
2016_05_15-PM-10_26_23
Last ObjectModification:
2015_12_27-PM-06_26_52
Theory : minimal-first-order-logic
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