Nuprl Lemma : path-comp-exists
∀G:j⊢. ∀A:{G ⊢ _}. ∀a,b:{G ⊢ _:A}. (G ⊢ CompOp(A) ⇒ G ⊢ CompOp((Path_A a b)))
Proof
Definitions occuring in Statement :
composition-op: Gamma ⊢ CompOp(A),
path-type: (Path_A a b),
cubical-term: {X ⊢ _:A},
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 :
composition-op-implies-composition-structure,
path_comp_wf,
composition-op_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
istype-cubical-term,
cubical-type_wf,
cubical_set_wf,
composition-structure-implies-composition-op,
path-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
rename,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
hypothesis,
universeIsType,
instantiate,
applyEquality,
sqequalRule,
inhabitedIsType,
independent_functionElimination
Latex:
\mforall{}G:j\mvdash{}. \mforall{}A:\{G \mvdash{} \_\}. \mforall{}a,b:\{G \mvdash{} \_:A\}. (G \mvdash{} CompOp(A) {}\mRightarrow{} G \mvdash{} CompOp((Path\_A a b)))
Date html generated:
2020_05_20-PM-05_12_23
Last ObjectModification:
2020_04_18-AM-09_57_23
Theory : cubical!type!theory
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