Nuprl Lemma : face-type-at
∀[J,rho:Top]. (𝔽(rho) ~ Point(face_lattice(J)))
Proof
Definitions occuring in Statement :
face-type: 𝔽,
cubical-type-at: A(a),
face_lattice: face_lattice(I),
lattice-point: Point(l),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
face-type: 𝔽,
cubical-type-at: A(a),
face-presheaf: 𝔽,
constant-cubical-type: (X),
pi1: fst(t),
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
top_wf,
I_cube_pair_redex_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[J,rho:Top]. (\mBbbF{}(rho) \msim{} Point(face\_lattice(J)))
Date html generated:
2016_05_19-AM-08_24_28
Last ObjectModification:
2016_03_03-PM-03_29_10
Theory : cubical!type!theory
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