Nuprl Lemma : mFOL-sequent-freevars-contains-concl
∀s:mFOL-sequent(). ∀L:ℤ List. (L ⊆ mFOL-freevars(snd(s)) ⇒ L ⊆ mFOL-sequent-freevars(s))
Proof
Definitions occuring in Statement :
mFOL-sequent-freevars: mFOL-sequent-freevars(s),
mFOL-sequent: mFOL-sequent(),
mFOL-freevars: mFOL-freevars(fmla),
l_contains: A ⊆ B,
list: T List,
pi2: snd(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
mFOL-sequent: mFOL-sequent(),
mFOL-sequent-freevars: mFOL-sequent-freevars(s),
pi2: snd(t),
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
top: Top,
guard: {T}
Lemmas referenced :
mFOL-freevars_wf,
list_wf,
list_induction,
mFOL_wf,
all_wf,
l_contains_wf,
reduce_wf,
l-union_wf,
int-deq_wf,
reduce_nil_lemma,
reduce_cons_lemma,
l-union-right-contains,
equal_wf,
mFOL-sequent_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
intEquality,
lambdaEquality,
functionEquality,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
rename,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}s:mFOL-sequent(). \mforall{}L:\mBbbZ{} List. (L \msubseteq{} mFOL-freevars(snd(s)) {}\mRightarrow{} L \msubseteq{} mFOL-sequent-freevars(s))
Date html generated:
2018_05_21-PM-10_29_33
Last ObjectModification:
2017_07_26-PM-06_41_42
Theory : minimal-first-order-logic
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