Nuprl Lemma : contractible-type-subset
∀[X,A,phi:Top]. (X, phi ⊢ Contractible(A) ~ X ⊢ Contractible(A))
Proof
Definitions occuring in Statement :
contractible-type: Contractible(A),
context-subset: Gamma, phi,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
contractible-type: Contractible(A),
cubical-pi: ΠA B,
cubical-sigma: Σ A B,
all: ∀x:A. B[x],
top: Top,
path-type: (Path_A a b),
cubical-pi-family: cubical-pi-family(X;A;B;I;a),
pathtype: Path(A),
cubical-subset: {t:T | ∀I,alpha. psi[I; alpha; t]},
cubical-fun: (A ⟶ B),
cubical-fun-family: cubical-fun-family(X; A; B; I; a),
cube-context-adjoin: X.A,
context-subset: Gamma, phi,
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
cubical_type_at_pair_lemma,
cubical_type_ap_morph_pair_lemma,
cube_set_restriction_pair_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[X,A,phi:Top]. (X, phi \mvdash{} Contractible(A) \msim{} X \mvdash{} Contractible(A))
Date html generated:
2018_05_23-AM-09_38_47
Last ObjectModification:
2018_05_20-PM-06_40_18
Theory : cubical!type!theory
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