Nuprl Lemma : rat-cube-face-decider_wf
∀k:ℕ. ∀c,d:ℚCube(k). (rat-cube-face-decider(k;c;d) ∈ Dec(c ≤ d))
Proof
Definitions occuring in Statement :
rat-cube-face-decider: rat-cube-face-decider(k;c;d),
rat-cube-face: c ≤ d,
rational-cube: ℚCube(k),
nat: ℕ,
decidable: Dec(P),
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
decidable__rat-cube-face-ext,
rat-cube-face-decider: rat-cube-face-decider(k;c;d),
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
istype-nat,
rat-cube-face_wf,
decidable_wf,
rational-cube_wf,
nat_wf,
subtype_rel_self,
decidable__rat-cube-face-ext
Rules used in proof :
universeIsType,
inhabitedIsType,
hypothesisEquality,
functionEquality,
isectElimination,
sqequalHypSubstitution,
introduction,
hypothesis,
extract_by_obid,
instantiate,
thin,
applyEquality,
sqequalRule,
cut,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}k:\mBbbN{}. \mforall{}c,d:\mBbbQ{}Cube(k). (rat-cube-face-decider(k;c;d) \mmember{} Dec(c \mleq{} d))
Date html generated:
2019_10_29-AM-07_50_04
Last ObjectModification:
2019_10_19-AM-10_44_47
Theory : rationals
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