Nuprl Lemma : face-forall-implies-csm+
∀[H:j⊢]. ∀[phi:{H.𝕀 ⊢ _:𝔽}]. ∀[K:j⊢]. ∀[tau:K j⟶ H]. K.𝕀 ⊢ ((((∀ phi))tau)p ⇒ (phi)tau+)
Proof
Definitions occuring in Statement :
face-forall: (∀ phi),
face-term-implies: Gamma ⊢ (phi ⇒ psi),
face-type: 𝔽,
interval-type: 𝕀,
csm+: tau+,
cc-fst: p,
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a
Lemmas referenced :
csm+_wf_interval,
face-forall-implies,
csm-ap-term_wf,
cube-context-adjoin_wf,
interval-type_wf,
face-type_wf,
cubical_set_cumulativity-i-j,
csm-face-type,
cube_set_map_wf,
cubical-term_wf,
cubical_set_wf,
cc-fst_wf,
csm-face-forall,
subset-cubical-term2,
sub_cubical_set_self,
csm-ap-type_wf,
equal_wf,
face-term-implies_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
instantiate,
applyEquality,
sqequalRule,
Error :memTop,
equalityTransitivity,
equalitySymmetry,
universeIsType,
inhabitedIsType,
because_Cache,
hyp_replacement,
applyLambdaEquality,
independent_isectElimination
Latex:
\mforall{}[H:j\mvdash{}]. \mforall{}[phi:\{H.\mBbbI{} \mvdash{} \_:\mBbbF{}\}]. \mforall{}[K:j\mvdash{}]. \mforall{}[tau:K j{}\mrightarrow{} H]. K.\mBbbI{} \mvdash{} ((((\mforall{} phi))tau)p {}\mRightarrow{} (phi)tau+)
Date html generated:
2020_05_20-PM-03_03_25
Last ObjectModification:
2020_04_06-AM-10_33_15
Theory : cubical!type!theory
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