Nuprl Lemma : mFOL-sequent-freevars-subset-2
∀hyps:mFOL() List. ∀concl,h:mFOL(). ((h ∈ hyps) ⇒ mFOL-freevars(h) ⊆ 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,
l_member: (x ∈ l),
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
pair: <a, b>,
int: ℤ
Definitions unfolded in proof :
mFOL-sequent-freevars: mFOL-sequent-freevars(s),
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
top: Top,
uimplies: b supposing a,
not: ¬A,
false: False,
iff: P ⇐⇒ Q,
and: P ∧ Q,
or: P ∨ Q
Lemmas referenced :
list_induction,
mFOL_wf,
all_wf,
l_member_wf,
l_contains_wf,
mFOL-freevars_wf,
reduce_wf,
list_wf,
l-union_wf,
int-deq_wf,
reduce_nil_lemma,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
nil_wf,
btrue_neq_bfalse,
reduce_cons_lemma,
cons_wf,
cons_member,
union-contains,
l_contains_transitivity,
union-contains2
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
lambdaEquality,
functionEquality,
hypothesisEquality,
intEquality,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
rename,
productElimination,
unionElimination,
hyp_replacement,
Error :applyLambdaEquality
Latex:
\mforall{}hyps:mFOL() List. \mforall{}concl,h:mFOL().
((h \mmember{} hyps) {}\mRightarrow{} mFOL-freevars(h) \msubseteq{} mFOL-sequent-freevars(<hyps, concl>))
Date html generated:
2016_10_25-AM-11_45_32
Last ObjectModification:
2016_07_12-AM-07_45_05
Theory : minimal-first-order-logic
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