Nuprl Lemma : ps-csm_id_adjoin_fst_type_lemma
∀A,t,X:Top. (((A)p)[t] ~ (A)1(X))
Proof
Definitions occuring in Statement :
pscm-id-adjoin: [u],
psc-fst: p,
pscm-ap-type: (AF)s,
pscm-id: 1(X),
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
pscm-id: 1(X),
pscm-ap-type: (AF)s,
psc-fst: p,
pscm-id-adjoin: [u],
pscm-ap: (s)x,
pscm-adjoin: (s;u),
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,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
hypothesis,
because_Cache
Latex:
\mforall{}A,t,X:Top. (((A)p)[t] \msim{} (A)1(X))
Date html generated:
2018_05_23-AM-08_13_28
Last ObjectModification:
2018_05_20-PM-09_52_37
Theory : presheaf!models!of!type!theory
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