Nuprl Lemma : ps-csm_typedp_id_adjoin_lemma
∀E,s,F,G,u,H:Top. ((((E)s)tp{i:l})[u] ~ (E)s)
Proof
Definitions occuring in Statement :
pscm-id-adjoin: [u],
typed-psc-fst: tp{i:l},
pscm-ap-type: (AF)s,
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
pscm-ap-type: (AF)s,
typed-psc-fst: tp{i:l},
pscm-id-adjoin: [u],
pscm-ap: (s)x,
pscm-id: 1(X),
pscm-adjoin: (s;u),
psc-fst: p,
uall: ∀[x:A]. B[x],
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,
pi1: fst(t)
Lemmas referenced :
lifting-strict-spread,
strict4-spread,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
hypothesis
Latex:
\mforall{}E,s,F,G,u,H:Top. ((((E)s)tp\{i:l\})[u] \msim{} (E)s)
Date html generated:
2018_05_23-AM-08_26_46
Last ObjectModification:
2018_05_20-PM-10_07_55
Theory : presheaf!models!of!type!theory
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