Nuprl Lemma : term-to-path-subset
∀[X,phi,a:Top]. (X, phi ⊢ <>(a) ~ X ⊢ <>(a))
Proof
Definitions occuring in Statement :
term-to-path: <>(a),
context-subset: Gamma, phi,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
term-to-path: <>(a),
context-subset: Gamma, phi,
cubical-lambda: (λb),
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x]
Lemmas referenced :
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{}[X,phi,a:Top]. (X, phi \mvdash{} <>(a) \msim{} X \mvdash{} <>(a))
Date html generated:
2018_05_23-AM-09_36_32
Last ObjectModification:
2018_05_20-PM-06_37_58
Theory : cubical!type!theory
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