Nuprl Lemma : equiv-comp-exists
∀H:j⊢. ∀A,E:{H ⊢ _}. (H ⊢ CompOp(A) ⇒ H ⊢ CompOp(E) ⇒ H ⊢ CompOp(Equiv(A;E)))
Proof
Definitions occuring in Statement :
composition-op: Gamma ⊢ CompOp(A),
cubical-equiv: Equiv(T;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 :
equiv-comp_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
composition-op_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
rename,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
sqequalRule,
universeIsType,
inhabitedIsType
Latex:
\mforall{}H:j\mvdash{}. \mforall{}A,E:\{H \mvdash{} \_\}. (H \mvdash{} CompOp(A) {}\mRightarrow{} H \mvdash{} CompOp(E) {}\mRightarrow{} H \mvdash{} CompOp(Equiv(A;E)))
Date html generated:
2020_05_20-PM-07_20_33
Last ObjectModification:
2020_04_25-PM-09_50_34
Theory : cubical!type!theory
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