Nuprl Lemma : composition-op-implies-composition-structure
∀Gamma:j⊢. ∀A:{Gamma ⊢ _}. ∀cA:Gamma ⊢ CompOp(A). Gamma ⊢ Compositon(A)
Proof
Definitions occuring in Statement :
composition-structure: Gamma ⊢ Compositon(A),
composition-op: Gamma ⊢ CompOp(A),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
comp-op-to-comp-fun_wf2,
composition-op_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeIsType,
instantiate,
applyEquality,
sqequalRule
Latex:
\mforall{}Gamma:j\mvdash{}. \mforall{}A:\{Gamma \mvdash{} \_\}. \mforall{}cA:Gamma \mvdash{} CompOp(A). Gamma \mvdash{} Compositon(A)
Date html generated:
2020_05_20-PM-04_27_15
Last ObjectModification:
2020_04_18-AM-09_55_48
Theory : cubical!type!theory
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