Nuprl Lemma : path_term-0
∀[H,A,psi,r,a,b,w:Top].
((path_term(psi; w; a; b; r))[0(𝕀)] ~ path-term((psi)1(H.A);(w)[0(𝕀)];(a)[0(𝕀)];(b)[0(𝕀)];(r)1(H.A)))
Proof
Definitions occuring in Statement :
path_term: path_term(phi; w; a; b; r),
path-term: path-term(phi;w;a;b;r),
interval-0: 0(𝕀),
csm-id-adjoin: [u],
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
csm-id: 1(X),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
all: ∀x:A. B[x]
Lemmas referenced :
csm-path_term,
csm_id_adjoin_fst_term_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
dependent_functionElimination,
because_Cache
Latex:
\mforall{}[H,A,psi,r,a,b,w:Top].
((path\_term(psi; w; a; b; r))[0(\mBbbI{})]
\msim{} path-term((psi)1(H.A);(w)[0(\mBbbI{})];(a)[0(\mBbbI{})];(b)[0(\mBbbI{})];(r)1(H.A)))
Date html generated:
2018_05_23-AM-11_00_49
Last ObjectModification:
2018_05_20-PM-08_04_35
Theory : cubical!type!theory
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