Nuprl Lemma : face-term-iff_wf
∀[Gamma:j⊢]. ∀[phi,psi:{Gamma ⊢ _:𝔽}]. (Gamma ⊢ (phi ⇐⇒ psi) ∈ ℙ{[i | j']})
Proof
Definitions occuring in Statement :
face-term-iff: Gamma ⊢ (phi ⇐⇒ psi),
face-type: 𝔽,
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
face-term-iff: Gamma ⊢ (phi ⇐⇒ psi),
prop: ℙ,
and: P ∧ Q
Lemmas referenced :
face-term-implies_wf,
cubical-term_wf,
face-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[phi,psi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. (Gamma \mvdash{} (phi \mLeftarrow{}{}\mRightarrow{} psi) \mmember{} \mBbbP{}\{[i | j']\})
Date html generated:
2020_05_20-PM-02_48_35
Last ObjectModification:
2020_04_04-PM-07_03_33
Theory : cubical!type!theory
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