Nuprl Lemma : pres-a0_wf
∀[G:j⊢]. ∀[A,T:{G.𝕀 ⊢ _}]. ∀[f:{G.𝕀 ⊢ _:(T ⟶ A)}]. ∀[t0:{G ⊢ _:(T)[0(𝕀)]}]. (pres-a0(G;f;t0) ∈ {G ⊢ _:(A)[0(𝕀)]})
Proof
Definitions occuring in Statement :
pres-a0: pres-a0(G;f;t0),
interval-0: 0(𝕀),
interval-type: 𝕀,
cubical-fun: (A ⟶ B),
csm-id-adjoin: [u],
cube-context-adjoin: X.A,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
uimplies: b supposing a,
pres-a0: pres-a0(G;f;t0)
Lemmas referenced :
csm-ap-term_wf,
cube-context-adjoin_wf,
interval-type_wf,
cubical-fun_wf,
csm-id-adjoin_wf-interval-0,
csm-cubical-fun,
csm-id-adjoin_wf,
interval-0_wf,
cubical-term-eqcd,
cubical-app_wf_fun,
csm-ap-type_wf,
cubical_set_cumulativity-i-j,
istype-cubical-term,
cubical-type-cumulativity2,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
sqequalRule,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
lambdaEquality_alt,
cumulativity,
universeIsType,
universeEquality,
hyp_replacement
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[A,T:\{G.\mBbbI{} \mvdash{} \_\}]. \mforall{}[f:\{G.\mBbbI{} \mvdash{} \_:(T {}\mrightarrow{} A)\}]. \mforall{}[t0:\{G \mvdash{} \_:(T)[0(\mBbbI{})]\}].
(pres-a0(G;f;t0) \mmember{} \{G \mvdash{} \_:(A)[0(\mBbbI{})]\})
Date html generated:
2020_05_20-PM-05_25_18
Last ObjectModification:
2020_04_18-PM-10_55_48
Theory : cubical!type!theory
Home
Index