Nuprl Lemma : csm-case-endpoints
∀[a,b,r,s:Top]. (([r=0 ⊢→ a; r=1 ⊢→ b])s ~ [(r)s=0 ⊢→ (a)s; (r)s=1 ⊢→ (b)s])
Proof
Definitions occuring in Statement :
case-endpoints: [r=0 ⊢→ a; r=1 ⊢→ b],
csm-ap-term: (t)s,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
case-endpoints: [r=0 ⊢→ a; r=1 ⊢→ b],
member: t ∈ T,
top: Top
Lemmas referenced :
top_wf,
csm-case-term,
csm-face-zero
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
because_Cache,
cut,
introduction,
extract_by_obid,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
sqequalRule,
sqequalHypSubstitution,
isectElimination,
thin
Latex:
\mforall{}[a,b,r,s:Top]. (([r=0 \mvdash{}\mrightarrow{} a; r=1 \mvdash{}\mrightarrow{} b])s \msim{} [(r)s=0 \mvdash{}\mrightarrow{} (a)s; (r)s=1 \mvdash{}\mrightarrow{} (b)s])
Date html generated:
2018_05_23-AM-10_19_30
Last ObjectModification:
2018_05_20-PM-07_20_14
Theory : cubical!type!theory
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