Nuprl Lemma : mFOL-sequent-freevars-subset-4
∀hyps:mFOL() List. ∀x,y:mFOL(). (mFOL-freevars(x) ⊆ mFOL-sequent-freevars(<hyps, y>) ⇒ mFOL-sequent-freevars(<hyps, x>\000C) ⊆ mFOL-sequent-freevars(<hyps, y>))
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],
implies: P ⇒ Q,
pair: <a, b>,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
mFOL-sequent: mFOL-sequent(),
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
pi2: snd(t),
pi1: fst(t),
prop: ℙ
Lemmas referenced :
mFOL-sequent-freevars-contained,
list_wf,
mFOL_wf,
mFOL-sequent-freevars_wf,
mFOL-sequent-freevars-subset-2,
l_member_wf,
l_contains_wf,
mFOL-freevars_wf
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,
because_Cache,
productElimination,
independent_functionElimination,
independent_pairFormation,
intEquality
Latex:
\mforall{}hyps:mFOL() List. \mforall{}x,y:mFOL(). (mFOL-freevars(x) \msubseteq{} mFOL-sequent-freevars(<hyps, y>) {}\mRightarrow{} mFOL-sequen\000Ct-freevars(<hyps, x>) \msubseteq{} mFOL-sequent-freevars(<hyps, y>))
Date html generated:
2016_05_15-PM-10_26_30
Last ObjectModification:
2015_12_27-PM-06_26_41
Theory : minimal-first-order-logic
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