Nuprl Lemma : csm-cubical-subset
∀[T,psi,s:Top]. (({t:T | ∀I,alpha. psi[I;alpha;t]})s ~ {t:(T)s | ∀I,alpha. psi[I;(s)alpha;t]})
Proof
Definitions occuring in Statement :
cubical-subset: {t:T | ∀I,alpha. psi[I; alpha; t]},
csm-ap-type: (AF)s,
csm-ap: (s)x,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2;s3],
sqequal: s ~ t
Definitions unfolded in proof :
pi2: snd(t),
cubical-type-ap-morph: (u a f),
so_apply: x[s1;s2;s3],
csm-ap: (s)x,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
squash: ↓T,
or: P ∨ Q,
guard: {T},
prop: ℙ,
has-value: (a)↓,
implies: P ⇒ Q,
all: ∀x:A. B[x],
and: P ∧ Q,
strict4: strict4(F),
uimplies: b supposing a,
top: Top,
so_apply: x[s1;s2;s3;s4],
member: t ∈ T,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
pi1: fst(t),
cubical-type-at: A(a),
cubical-subset: {t:T | ∀I,alpha. psi[I; alpha; t]},
csm-ap-type: (AF)s,
uall: ∀[x:A]. B[x]
Lemmas referenced :
top_wf,
strict4-spread,
is-exception_wf,
base_wf,
has-value_wf_base,
lifting-strict-spread
Rules used in proof :
because_Cache,
inlFormation,
exceptionSqequal,
imageElimination,
imageMemberEquality,
inrFormation,
applyExceptionCases,
hypothesisEquality,
closedConclusion,
baseApply,
hypothesis,
callbyvalueApply,
lambdaFormation,
independent_pairFormation,
independent_isectElimination,
voidEquality,
voidElimination,
isect_memberEquality,
baseClosed,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
sqequalRule,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T,psi,s:Top]. ((\{t:T | \mforall{}I,alpha. psi[I;alpha;t]\})s \msim{} \{t:(T)s | \mforall{}I,alpha. psi[I;(s)alpha;t]\})
Date html generated:
2016_07_09-PM-01_31_48
Last ObjectModification:
2016_07_09-AM-11_08_04
Theory : cubical!type!theory
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