Nuprl Lemma : squash-from-quotient
∀[Q:ℙ]. (⇃(Q) ⇒ (↓Q))
Proof
Definitions occuring in Statement :
quotient: x,y:A//B[x; y],
uall: ∀[x:A]. B[x],
prop: ℙ,
squash: ↓T,
implies: P ⇒ Q,
true: True
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
guard: {T}
Lemmas referenced :
quotient_wf,
true_wf,
equiv_rel_true,
quotient-implies-squash
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
imageElimination,
hypothesis,
imageMemberEquality,
baseClosed,
extract_by_obid,
isectElimination,
cumulativity,
because_Cache,
independent_isectElimination,
universeEquality,
lambdaFormation,
independent_functionElimination
Latex:
\mforall{}[Q:\mBbbP{}]. (\00D9(Q) {}\mRightarrow{} (\mdownarrow{}Q))
Date html generated:
2016_12_12-AM-09_14_52
Last ObjectModification:
2016_11_22-PM-01_50_34
Theory : quot_1
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