Nuprl Lemma : ps-sigma-unelim-p-type
∀[T:Top]. (((T)p)SigmaUnElim ~ ((T)p)p)
Proof
Definitions occuring in Statement :
sigma-unelim-pscm: SigmaUnElim,
psc-fst: p,
pscm-ap-type: (AF)s,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sigma-unelim-pscm: SigmaUnElim,
psc-fst: p,
pscm-ap-type: (AF)s,
psc-adjoin-set: (v;u),
pscm-ap: (s)x,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
uimplies: b supposing a,
pi1: fst(t)
Lemmas referenced :
top_wf,
lifting-strict-spread,
strict4-spread
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalAxiom,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination
Latex:
\mforall{}[T:Top]. (((T)p)SigmaUnElim \msim{} ((T)p)p)
Date html generated:
2018_05_23-AM-08_22_08
Last ObjectModification:
2018_05_20-PM-10_03_01
Theory : presheaf!models!of!type!theory
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