Nuprl Lemma : p-pscm+-type
∀[H,K,A,B,tau:Top]. (((A)p)tau+ ~ ((A)tau)p)
Proof
Definitions occuring in Statement :
pscm+: tau+,
psc-fst: p,
pscm-ap-type: (AF)s,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
pscm-ap-type: (AF)s,
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,
pscm-ap: (s)x,
psc-fst: p,
pi1: fst(t),
pscm+: tau+,
pscm-adjoin: (s;u),
pscm-comp: G o F,
compose: f o g
Lemmas referenced :
top_wf,
lifting-strict-spread,
strict4-spread
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
hypothesis,
because_Cache,
isect_memberFormation,
sqequalAxiom,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
baseClosed,
voidElimination,
voidEquality,
independent_isectElimination
Latex:
\mforall{}[H,K,A,B,tau:Top]. (((A)p)tau+ \msim{} ((A)tau)p)
Date html generated:
2018_05_23-AM-08_14_13
Last ObjectModification:
2018_05_20-PM-09_53_21
Theory : presheaf!models!of!type!theory
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