Nuprl Lemma : sp-le_wf
∀[x,y:Sierpinski]. (x ≤ y ∈ ℙ)
Proof
Definitions occuring in Statement :
sp-le: x ≤ y,
Sierpinski: Sierpinski,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sp-le: x ≤ y,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
equal_wf,
Sierpinski_wf,
Sierpinski-top_wf,
subtype-Sierpinski
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
functionEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
applyEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[x,y:Sierpinski]. (x \mleq{} y \mmember{} \mBbbP{})
Date html generated:
2019_10_31-AM-06_36_04
Last ObjectModification:
2015_12_28-AM-11_21_15
Theory : synthetic!topology
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