Nuprl Lemma : csm-m-comp-1
∀[H:j⊢]. (m o [1(𝕀)] = 1(H.𝕀) ∈ H.𝕀 ij⟶ H.𝕀)
Proof
Definitions occuring in Statement :
csm-m: m,
interval-1: 1(𝕀),
interval-type: 𝕀,
csm-id-adjoin: [u],
cube-context-adjoin: X.A,
csm-id: 1(X),
csm-comp: G o F,
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
cube-context-adjoin: X.A,
interval-presheaf: 𝕀,
csm-id: 1(X),
csm-m: m,
interval-1: 1(𝕀),
interval-type: 𝕀,
csm-id-adjoin: [u],
csm-comp: G o F,
compose: f o g,
csm-adjoin: (s;u),
csm-ap: (s)x,
cc-adjoin-cube: (v;u),
dM1: 1,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
cubical_set_wf,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
interval-type_wf,
csm-comp_wf,
csm-id-adjoin_wf-interval-1,
csm-m_wf,
csm-id_wf,
I_cube_pair_redex_lemma,
cube_set_restriction_pair_lemma,
I_cube_wf,
fset_wf,
nat_wf,
lattice-meet-1,
dM_wf,
bdd-distributive-lattice-subtype-bdd-lattice,
DeMorgan-algebra-subtype,
subtype_rel_transitivity,
DeMorgan-algebra_wf,
bdd-distributive-lattice_wf,
bdd-lattice_wf,
csm-equal2,
interval-type-at
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
universeIsType,
cut,
instantiate,
introduction,
extract_by_obid,
hypothesis,
thin,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
sqequalRule,
because_Cache,
lambdaFormation_alt,
dependent_functionElimination,
Error :memTop,
productElimination,
dependent_pairEquality_alt,
independent_isectElimination,
inhabitedIsType
Latex:
\mforall{}[H:j\mvdash{}]. (m o [1(\mBbbI{})] = 1(H.\mBbbI{}))
Date html generated:
2020_05_20-PM-04_42_52
Last ObjectModification:
2020_04_10-AM-11_24_31
Theory : cubical!type!theory
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