Nuprl Lemma : mFOL-sequent-freevars-subset-3
∀hyps:mFOL() List. ∀x,y:mFOL().  (mFOL-freevars(x) ⊆ mFOL-freevars(y) 
⇒ mFOL-sequent-freevars(<hyps, x>) ⊆ mFOL-sequent\000C-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]
, 
pi2: snd(t)
, 
prop: ℙ
Lemmas referenced : 
mFOL-sequent-freevars-subset-4, 
mFOL-sequent-freevars-contains-concl, 
list_wf, 
mFOL_wf, 
mFOL-freevars_wf, 
l_contains_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
independent_functionElimination, 
independent_pairEquality, 
hypothesis, 
applyEquality, 
lambdaEquality, 
sqequalRule, 
productEquality, 
isectElimination, 
intEquality
Latex:
\mforall{}hyps:mFOL()  List.  \mforall{}x,y:mFOL().
    (mFOL-freevars(x)  \msubseteq{}  mFOL-freevars(y)  {}\mRightarrow{}  mFOL-sequent-freevars(<hyps,  x>)  \msubseteq{}  mFOL-sequent-freevars(<\000Chyps,  y>))
Date html generated:
2016_05_15-PM-10_26_32
Last ObjectModification:
2015_12_27-PM-06_26_34
Theory : minimal-first-order-logic
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