Nuprl Lemma : cubical-isect-subset-adjoin2

∀[X,phi,A,B,C,D:Top].  (⋂A B ~ ⋂A B)


Proof




Definitions occuring in Statement :  cubical-isect: ⋂A B,  context-subset: Gamma, phi,  cube-context-adjoin: X.A,  uall: ∀[x:A]. B[x],  top: Top,  sqequal: s ~ t
Definitions unfolded in proof :  cube-context-adjoin: X.A,  cubical-isect: ⋂A B,  context-subset: Gamma, phi,  all: ∀x:A. B[x],  member: t ∈ T,  top: Top,  cubical-isect-family: cubical-isect-family(X;A;B;I;a),  uall: ∀[x:A]. B[x]
Lemmas referenced :  I_cube_pair_redex_lemma,  cube_set_restriction_pair_lemma,  top_wf
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  sqequalRule,  cut,  introduction,  extract_by_obid,  sqequalHypSubstitution,  dependent_functionElimination,  thin,  isect_memberEquality,  voidElimination,  voidEquality,  hypothesis,  because_Cache,  isect_memberFormation,  sqequalAxiom,  isectElimination,  hypothesisEquality

Latex:
\mforall{}[X,phi,A,B,C,D:Top].    (\mcap{}A  B  \msim{}  \mcap{}A  B)



Date html generated: 2017_01_10-PM-00_27_36
Last ObjectModification: 2017_01_06-PM-02_57_51

Theory : cubical!type!theory


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