Nuprl Lemma : context-subset_functionality
∀[Gamma:j⊢]. ∀[a,b:{Gamma ⊢ _:𝔽}]. (Gamma ⊢ (a ⇐⇒ b) ⇒ {Gamma, a ⊢ _} ≡ {Gamma, b ⊢ _})
Proof
Definitions occuring in Statement :
face-term-iff: Gamma ⊢ (phi ⇐⇒ psi),
context-subset: Gamma, phi,
face-type: 𝔽,
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
face-term-iff: Gamma ⊢ (phi ⇐⇒ psi),
and: P ∧ Q,
ext-eq: A ≡ B,
uimplies: b supposing a,
face-term-implies: Gamma ⊢ (phi ⇒ psi),
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
context-subset-subtype,
face-term-iff_wf,
cubical-term_wf,
face-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
extract_by_obid,
isectElimination,
hypothesisEquality,
independent_isectElimination,
hypothesis,
because_Cache,
universeIsType,
instantiate,
sqequalRule,
lambdaEquality_alt,
dependent_functionElimination,
independent_pairEquality,
axiomEquality,
functionIsTypeImplies,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[a,b:\{Gamma \mvdash{} \_:\mBbbF{}\}]. (Gamma \mvdash{} (a \mLeftarrow{}{}\mRightarrow{} b) {}\mRightarrow{} \{Gamma, a \mvdash{} \_\} \mequiv{} \{Gamma, b \mvdash{} \_\})
Date html generated:
2020_05_20-PM-02_51_36
Last ObjectModification:
2020_04_06-AM-10_32_20
Theory : cubical!type!theory
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