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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