Nuprl Lemma : fun-comp-exists
∀Gamma:j⊢. ∀A,B:{Gamma ⊢ _}. (Gamma ⊢ CompOp(A) ⇒ Gamma ⊢ CompOp(B) ⇒ Gamma ⊢ CompOp((A ⟶ B)))
Proof
Definitions occuring in Statement :
composition-op: Gamma ⊢ CompOp(A),
cubical-fun: (A ⟶ B),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
fun-comp_wf,
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,
rename,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeIsType,
instantiate,
applyEquality,
sqequalRule,
because_Cache,
inhabitedIsType
Latex:
\mforall{}Gamma:j\mvdash{}. \mforall{}A,B:\{Gamma \mvdash{} \_\}. (Gamma \mvdash{} CompOp(A) {}\mRightarrow{} Gamma \mvdash{} CompOp(B) {}\mRightarrow{} Gamma \mvdash{} CompOp((A {}\mrightarrow{} B)))
Date html generated:
2020_05_20-PM-04_04_33
Last ObjectModification:
2020_04_10-AM-01_43_02
Theory : cubical!type!theory
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