Nuprl Lemma : sp-join-com
∀[x,y:Sierpinski]. (x ∨ y = y ∨ x ∈ Sierpinski)
Proof
Definitions occuring in Statement :
sp-join: 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,
rev_implies: P ⇐ Q,
cand: A c∧ B,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
Sierpinski-equal,
sp-join_wf,
sp-join-is-bottom,
equal_wf,
Sierpinski_wf,
Sierpinski-bottom_wf,
subtype-Sierpinski
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
independent_functionElimination,
applyEquality,
sqequalRule,
because_Cache,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[x,y:Sierpinski]. (x \mvee{} y = y \mvee{} x)
Date html generated:
2019_10_31-AM-06_36_33
Last ObjectModification:
2015_12_28-AM-11_21_00
Theory : synthetic!topology
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