Nuprl Lemma : path-type-subset-adjoin3
∀[X,T1,T2,T3,A,w,a,phi:Top]. ((X, phi.T1.T2.T3 ⊢ Path_A a w) ~ (X.T1.T2.T3 ⊢ Path_A a w))
Proof
Definitions occuring in Statement :
path-type: (Path_A a b),
context-subset: Gamma, phi,
cube-context-adjoin: X.A,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
path-type: (Path_A a b),
cubical-subset: {t:T | ∀I,alpha. psi[I; alpha; t]},
pathtype: Path(A),
cube-context-adjoin: X.A,
cubical-fun: (A ⟶ B),
context-subset: Gamma, phi,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
cubical-fun-family: cubical-fun-family(X; A; B; I; a),
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
cubical_type_at_pair_lemma,
I_cube_pair_redex_lemma,
cube_set_restriction_pair_lemma,
cubical_type_ap_morph_pair_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
because_Cache
Latex:
\mforall{}[X,T1,T2,T3,A,w,a,phi:Top]. ((X, phi.T1.T2.T3 \mvdash{} Path\_A a w) \msim{} (X.T1.T2.T3 \mvdash{} Path\_A a w))
Date html generated:
2017_01_10-AM-08_52_51
Last ObjectModification:
2016_12_11-PM-02_10_45
Theory : cubical!type!theory
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