Nuprl Lemma : half-squash-stable_wf
∀[P:ℙ]. (half-squash-stable(P) ∈ ℙ)
Proof
Definitions occuring in Statement :
half-squash-stable: half-squash-stable(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
prop: ℙ,
implies: P ⇒ Q,
half-squash-stable: half-squash-stable(P),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
equiv_rel_true,
true_wf,
quotient_wf
Rules used in proof :
universeEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
independent_isectElimination,
because_Cache,
hypothesis,
lambdaEquality,
hypothesisEquality,
cumulativity,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
functionEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[P:\mBbbP{}]. (half-squash-stable(P) \mmember{} \mBbbP{})
Date html generated:
2017_09_29-PM-05_48_09
Last ObjectModification:
2017_08_30-AM-10_28_59
Theory : quot_1
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