Nuprl Lemma : sq_stable-implies-half-squash-stable
∀[P:ℙ]. (SqStable(P) ⇒ half-squash-stable(P))
Proof
Definitions occuring in Statement :
half-squash-stable: half-squash-stable(P),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
prop: ℙ,
member: t ∈ T,
sq_stable: SqStable(P),
half-squash-stable: half-squash-stable(P),
implies: P ⇒ Q,
uall: ∀[x:A]. B[x]
Lemmas referenced :
squash-from-quotient,
sq_stable_wf,
equiv_rel_true,
true_wf,
quotient_wf
Rules used in proof :
universeEquality,
independent_isectElimination,
because_Cache,
lambdaEquality,
sqequalRule,
hypothesisEquality,
cumulativity,
isectElimination,
extract_by_obid,
introduction,
cut,
hypothesis,
thin,
independent_functionElimination,
sqequalHypSubstitution,
lambdaFormation,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[P:\mBbbP{}]. (SqStable(P) {}\mRightarrow{} half-squash-stable(P))
Date html generated:
2017_09_29-PM-05_48_12
Last ObjectModification:
2017_08_30-AM-11_02_23
Theory : quot_1
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