Nuprl Lemma : pscm-adjoin-id-adjoin
∀[B,xx,s,X,Y,Z:Top]. (((B)(s o p;q))[xx] ~ (B)(s;xx))
Proof
Definitions occuring in Statement :
pscm-id-adjoin: [u],
pscm-adjoin: (s;u),
psc-snd: q,
psc-fst: p,
pscm-ap-type: (AF)s,
pscm-comp: G o F,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
pscm-ap-type: (AF)s,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
member: t ∈ T,
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,
pscm-adjoin: (s;u),
pscm-comp: G o F,
compose: f o g,
psc-fst: p,
pi1: fst(t),
pscm-id-adjoin: [u],
pscm-id: 1(X),
psc-snd: q,
pi2: snd(t)
Lemmas referenced :
lifting-strict-spread,
strict4-spread,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
hypothesis,
because_Cache
Latex:
\mforall{}[B,xx,s,X,Y,Z:Top]. (((B)(s o p;q))[xx] \msim{} (B)(s;xx))
Date html generated:
2018_05_23-AM-08_14_04
Last ObjectModification:
2018_05_20-PM-09_53_15
Theory : presheaf!models!of!type!theory
Home
Index