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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