Nuprl Lemma : interval-type-at-is-point
∀[J,rho:Top]. (𝕀(rho) ~ Point(dM(J)))
Proof
Definitions occuring in Statement :
interval-type: 𝕀,
cubical-type-at: A(a),
dM: dM(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,
interval-presheaf: 𝕀,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
interval-type-at,
I_cube_pair_redex_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[J,rho:Top]. (\mBbbI{}(rho) \msim{} Point(dM(J)))
Date html generated:
2018_05_23-AM-09_18_38
Last ObjectModification:
2018_05_20-PM-06_17_14
Theory : cubical!type!theory
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