Nuprl Lemma : decidable__equal_rc
∀k:ℕ. ∀x,y:ℚCube(k). Dec(x = y ∈ ℚCube(k))
Proof
Definitions occuring in Statement :
rational-cube: ℚCube(k),
nat: ℕ,
decidable: Dec(P),
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
guard: {T},
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
istype-nat,
rc-deq_wf,
rational-cube_wf,
deq-implies
Rules used in proof :
independent_functionElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}k:\mBbbN{}. \mforall{}x,y:\mBbbQ{}Cube(k). Dec(x = y)
Date html generated:
2019_10_29-AM-07_49_02
Last ObjectModification:
2019_10_21-PM-03_42_26
Theory : rationals
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