Nuprl Lemma : ps-csm_dep_p_rewrite_lemma
∀T,s,A,Delta,X:Top. (((T)p)(s)dep ~ ((T)s)p)
Proof
Definitions occuring in Statement :
pscm-dependent: (s)dep,
psc-fst: p,
pscm-ap-type: (AF)s,
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
pscm-ap-type: (AF)s,
uall: ∀[x:A]. B[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,
pscm-ap: (s)x,
psc-fst: p,
pi1: fst(t),
pscm-dependent: (s)dep,
pscm-adjoin: (s;u),
pscm-comp: G o F,
compose: f o g,
typed-psc-fst: tp{i:l}
Lemmas referenced :
top_wf,
lifting-strict-spread,
strict4-spread
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalRule,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination
Latex:
\mforall{}T,s,A,Delta,X:Top. (((T)p)(s)dep \msim{} ((T)s)p)
Date html generated:
2018_05_23-AM-08_16_00
Last ObjectModification:
2018_05_20-PM-09_56_15
Theory : presheaf!models!of!type!theory
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