Nuprl Lemma : mFOL-freevars-connect-contained
∀x,y:mFOL(). ∀knd:Atom. ∀vs:ℤ List.
((mFOL-freevars(x) ⊆ vs ∧ mFOL-freevars(y) ⊆ vs) ⇒ mFOL-freevars(mFOconnect(knd;x;y)) ⊆ vs)
Proof
Definitions occuring in Statement :
mFOL-freevars: mFOL-freevars(fmla),
mFOconnect: mFOconnect(knd;left;right),
mFOL: mFOL(),
l_contains: A ⊆ B,
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
int: ℤ,
atom: Atom
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
mFOL-freevars: mFOL-freevars(fmla),
mFOconnect: mFOconnect(knd;left;right),
mFOL_ind: mFOL_ind,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B
Lemmas referenced :
val-union-l-union,
int-deq_wf,
mFOL-freevars_wf,
int-valueall-type,
and_wf,
l_contains_wf,
list_wf,
mFOL_wf,
l-union-contained
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
cut,
lemma_by_obid,
isectElimination,
intEquality,
hypothesis,
hypothesisEquality,
independent_isectElimination,
atomEquality,
dependent_functionElimination,
independent_functionElimination,
independent_pairFormation
Latex:
\mforall{}x,y:mFOL(). \mforall{}knd:Atom. \mforall{}vs:\mBbbZ{} List.
((mFOL-freevars(x) \msubseteq{} vs \mwedge{} mFOL-freevars(y) \msubseteq{} vs) {}\mRightarrow{} mFOL-freevars(mFOconnect(knd;x;y)) \msubseteq{} vs)
Date html generated:
2016_05_15-PM-10_14_45
Last ObjectModification:
2015_12_27-PM-06_32_17
Theory : minimal-first-order-logic
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