Nuprl Lemma : comp-op-to-comp-fun_wf2
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[cA:Gamma ⊢ CompOp(A)]. (cop-to-cfun(cA) ∈ Gamma ⊢ Compositon(A))
Proof
Definitions occuring in Statement :
comp-op-to-comp-fun: cop-to-cfun(cA),
composition-structure: Gamma ⊢ Compositon(A),
composition-op: Gamma ⊢ CompOp(A),
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,
composition-structure: Gamma ⊢ Compositon(A),
uniform-comp-function: uniform-comp-function{j:l, i:l}(Gamma; A; comp),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
csm-id-adjoin: [u],
csm-id: 1(X),
prop: ℙ
Lemmas referenced :
uniform-comp-function_wf,
comp-op-to-comp-fun_wf,
csm-comp-op-to-comp-fun,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
cube_set_map_cumulativity-i-j,
cube-context-adjoin_wf,
interval-type_wf,
constrained-cubical-term_wf,
csm-ap-type_wf,
csm-id-adjoin_wf-interval-0,
csm-ap-term_wf,
context-subset_wf,
thin-context-subset-adjoin,
istype-cubical-term,
csm-context-subset-subtype3,
face-type_wf,
cube_set_map_wf,
composition-op_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality_alt,
lambdaFormation_alt,
instantiate,
because_Cache,
applyEquality,
sqequalRule,
universeIsType,
inhabitedIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[cA:Gamma \mvdash{} CompOp(A)]. (cop-to-cfun(cA) \mmember{} Gamma \mvdash{} Compositon(A))
Date html generated:
2020_05_20-PM-04_27_02
Last ObjectModification:
2020_04_17-PM-08_46_58
Theory : cubical!type!theory
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