Nuprl Lemma : cubical-fun-subset-adjoin
∀[G,B,phi,T,A:Top]. ((G, phi.B ⊢ T ⟶ A) ~ (G.B ⊢ T ⟶ A))
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
cubical-fun: (A ⟶ B),
cube-context-adjoin: X.A,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
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),
uall: ∀[x:A]. B[x]
Lemmas referenced :
I_cube_pair_redex_lemma,
cube_set_restriction_pair_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[G,B,phi,T,A:Top]. ((G, phi.B \mvdash{} T {}\mrightarrow{} A) \msim{} (G.B \mvdash{} T {}\mrightarrow{} A))
Date html generated:
2018_05_23-AM-09_21_33
Last ObjectModification:
2018_05_20-PM-06_19_45
Theory : cubical!type!theory
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