Nuprl Lemma : sp-meet-assoc
∀[x,y,z:Sierpinski]. (x ∧ y ∧ z = x ∧ y ∧ z ∈ Sierpinski)
Proof
Definitions occuring in Statement :
sp-meet: f ∧ g,
Sierpinski: Sierpinski,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
cand: A c∧ B,
rev_implies: P ⇐ Q,
prop: ℙ
Lemmas referenced :
Sierpinski-equal2,
sp-meet_wf,
sp-meet-is-top,
equal-wf-T-base,
Sierpinski_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
addLevel,
independent_functionElimination,
levelHypothesis,
promote_hyp,
andLevelFunctionality,
because_Cache,
productEquality,
baseClosed,
sqequalRule,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[x,y,z:Sierpinski]. (x \mwedge{} y \mwedge{} z = x \mwedge{} y \mwedge{} z)
Date html generated:
2019_10_31-AM-06_36_35
Last ObjectModification:
2017_07_28-AM-09_12_16
Theory : synthetic!topology
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