Nuprl Lemma : decidable__compatible-rat-cubes
∀k:ℕ. ∀c,d:ℚCube(k).  Dec(Compatible(c;d))
Proof
Definitions occuring in Statement : 
compatible-rat-cubes: Compatible(c;d)
, 
rational-cube: ℚCube(k)
, 
nat: ℕ
, 
decidable: Dec(P)
, 
all: ∀x:A. B[x]
Definitions unfolded in proof : 
cand: A c∧ B
, 
implies: P 
⇒ Q
, 
and: P ∧ Q
, 
prop: ℙ
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
compatible-rat-cubes: Compatible(c;d)
Lemmas referenced : 
istype-nat, 
rational-cube_wf, 
decidable__rat-cube-face, 
decidable__cand, 
rat-cube-face_wf, 
rat-cube-intersection_wf, 
inhabited-rat-cube_wf, 
decidable__implies_better
Rules used in proof : 
inhabitedIsType, 
because_Cache, 
independent_functionElimination, 
universeIsType, 
productEquality, 
isect_memberEquality_alt, 
dependent_functionElimination, 
hypothesis, 
hypothesisEquality, 
thin, 
isectElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
introduction, 
cut, 
lambdaFormation_alt, 
computationStep, 
sqequalTransitivity, 
sqequalReflexivity, 
sqequalRule, 
sqequalSubstitution
Latex:
\mforall{}k:\mBbbN{}.  \mforall{}c,d:\mBbbQ{}Cube(k).    Dec(Compatible(c;d))
Date html generated:
2019_10_29-AM-07_54_37
Last ObjectModification:
2019_10_17-PM-01_46_32
Theory : rationals
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