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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