Nuprl Lemma : ex-approx_transitivity
∀[e:Atom2]. ∀[t1,t2,t3:Base].  (ex-approx(e;t1;t3)) supposing (ex-approx(e;t1;t2) and ex-approx(e;t2;t3))
Proof
Definitions occuring in Statement : 
ex-approx: ex-approx(e;t;t')
, 
atom: Atom$n
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
base: Base
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
uimplies: b supposing a
, 
member: t ∈ T
, 
sq_stable: SqStable(P)
, 
implies: P 
⇒ Q
, 
ex-approx: ex-approx(e;t;t')
, 
squash: ↓T
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
subtype_rel: A ⊆r B
Lemmas referenced : 
sq_stable__ex-approx, 
ex-approx_wf, 
base_wf, 
free-from-atom_wf2, 
sqle_trans, 
atom2_subtype_base
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
independent_functionElimination, 
sqequalRule, 
imageMemberEquality, 
baseClosed, 
imageElimination, 
because_Cache, 
atomnEquality, 
lambdaFormation, 
dependent_functionElimination, 
baseApply, 
closedConclusion, 
applyEquality
Latex:
\mforall{}[e:Atom2].  \mforall{}[t1,t2,t3:Base].
    (ex-approx(e;t1;t3))  supposing  (ex-approx(e;t1;t2)  and  ex-approx(e;t2;t3))
Date html generated:
2017_02_20-AM-10_56_47
Last ObjectModification:
2017_01_19-PM-05_24_23
Theory : minimal-first-order-logic
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