Nuprl Lemma : decidable__rat-cube-face
∀k:ℕ. ∀c,d:ℚCube(k). Dec(c ≤ d)
Proof
Definitions occuring in Statement :
rat-cube-face: c ≤ d,
rational-cube: ℚCube(k),
nat: ℕ,
decidable: Dec(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
implies: P ⇒ Q,
so_apply: x[s],
rational-cube: ℚCube(k),
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
nat: ℕ,
member: t ∈ T,
all: ∀x:A. B[x],
rat-cube-face: c ≤ d
Lemmas referenced :
istype-nat,
rational-cube_wf,
decidable__rat-interval-face,
int_seg_wf,
rat-interval-face_wf,
decidable__all_int_seg
Rules used in proof :
inhabitedIsType,
independent_functionElimination,
because_Cache,
universeIsType,
applyEquality,
lambdaEquality_alt,
isectElimination,
hypothesis,
hypothesisEquality,
rename,
setElimination,
natural_numberEquality,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
instantiate,
thin,
cut,
lambdaFormation_alt,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}k:\mBbbN{}. \mforall{}c,d:\mBbbQ{}Cube(k). Dec(c \mleq{} d)
Date html generated:
2019_10_29-AM-07_49_45
Last ObjectModification:
2019_10_19-AM-10_27_51
Theory : rationals
Home
Index