Nuprl Lemma : csm-type-at
∀Gamma:CubicalSet. ∀s:Top. ∀A:{Gamma ⊢ _}. ∀I,alpha:Top. ((A)s(alpha) ~ A((s)alpha))
Proof
Definitions occuring in Statement :
csm-ap-type: (AF)s,
cubical-type-at: A(a),
cubical-type: {X ⊢ _},
csm-ap: (s)x,
cubical-set: CubicalSet,
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
cubical-type: {X ⊢ _},
cubical-type-at: A(a),
csm-ap-type: (AF)s,
pi1: fst(t),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
top_wf,
cubical-type_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
hypothesis,
lemma_by_obid,
isectElimination,
hypothesisEquality
Latex:
\mforall{}Gamma:CubicalSet. \mforall{}s:Top. \mforall{}A:\{Gamma \mvdash{} \_\}. \mforall{}I,alpha:Top. ((A)s(alpha) \msim{} A((s)alpha))
Date html generated:
2016_06_16-PM-05_41_21
Last ObjectModification:
2015_12_28-PM-04_34_41
Theory : cubical!sets
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