Nuprl Lemma : ex-sqle_transitivity
∀[e:Atom2]. ∀[a,b,c:Base]. (ex-sqle(e;a;c)) supposing (ex-sqle(e;b;c) and ex-sqle(e;a;b))
Proof
Definitions occuring in Statement :
ex-sqle: ex-sqle(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],
member: t ∈ T,
uimplies: b supposing a,
ex-sqle: ex-sqle(e;t;t'),
prop: ℙ,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
implies: P ⇒ Q
Lemmas referenced :
ex-sqle_wf,
base_wf,
sqle_trans,
atom2_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
axiomSqleEquality,
hypothesis,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
atomnEquality,
dependent_functionElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
independent_functionElimination
Latex:
\mforall{}[e:Atom2]. \mforall{}[a,b,c:Base]. (ex-sqle(e;a;c)) supposing (ex-sqle(e;b;c) and ex-sqle(e;a;b))
Date html generated:
2017_02_20-AM-10_46_43
Last ObjectModification:
2017_01_25-PM-05_03_23
Theory : call!by!value_1
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