Nuprl Lemma : comp_term-composition-term
∀[Gamma,phi,cA,u,a0:Top]. (comp cop-to-cfun(cA) [phi ⊢→ u] a0 ~ comp cA [phi ⊢→ u] a0)
Proof
Definitions occuring in Statement :
comp_term: comp cA [phi ⊢→ u] a0,
comp-op-to-comp-fun: cop-to-cfun(cA),
composition-term: comp cA [phi ⊢→ u] a0,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
composition-term: comp cA [phi ⊢→ u] a0,
comp-op-to-comp-fun: cop-to-cfun(cA),
comp_term: comp cA [phi ⊢→ u] a0,
csm-composition: (comp)sigma,
cubical-term-at: u(a),
cc-adjoin-cube: (v;u),
subset-iota: iota,
csm-comp: G o F,
csm-ap-term: (t)s,
csm-id: 1(X),
csm-ap: (s)x,
compose: f o g,
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
because_Cache,
cut,
introduction,
extract_by_obid,
hypothesis
Latex:
\mforall{}[Gamma,phi,cA,u,a0:Top]. (comp cop-to-cfun(cA) [phi \mvdash{}\mrightarrow{} u] a0 \msim{} comp cA [phi \mvdash{}\mrightarrow{} u] a0)
Date html generated:
2018_05_23-AM-10_33_47
Last ObjectModification:
2018_05_20-PM-07_39_55
Theory : cubical!type!theory
Home
Index