Nuprl Lemma : decidable__rat-cube-face-ext
∀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 :
has-value: (a)↓,
implies: P ⇒ Q,
all: ∀x:A. B[x],
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
uimplies: b supposing a,
so_apply: x[s],
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s1;s2;s3;s4],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
uall: ∀[x:A]. B[x],
decidable__false,
decidable__equal_set,
decidable__equal_rationals,
decidable__equal_product,
decidable__implies,
any: any x,
decidable__equal_rational-interval,
decidable__or,
decidable__not,
decidable__exists_int_seg,
decidable__rat-interval-face,
decidable__all_int_seg,
decidable__rat-cube-face,
rat-cube-face-decider: rat-cube-face-decider(k;c;d),
ifunion: ifunion(b; t),
rat-point-interval: [a],
ifthenelse: if b then t else f fi ,
it: ⋅,
member: t ∈ T
Lemmas referenced :
is-exception_wf,
has-value_wf_base,
lifting-strict-decide,
lifting-strict-spread,
strict4-decide,
istype-void,
lifting-strict-callbyvalue,
decidable__rat-cube-face,
decidable__false,
decidable__equal_set,
decidable__equal_rationals,
decidable__equal_product,
decidable__implies,
decidable__equal_rational-interval,
decidable__or,
decidable__not,
decidable__exists_int_seg,
decidable__rat-interval-face,
decidable__all_int_seg
Rules used in proof :
decideExceptionCases,
unionElimination,
callbyvalueDecide,
because_Cache,
closedConclusion,
baseApply,
exceptionSqequal,
axiomSqleEquality,
spreadExceptionCases,
independent_functionElimination,
dependent_functionElimination,
hypothesisEquality,
equalityIstype,
sqleReflexivity,
productElimination,
callbyvalueSpread,
divergentSqle,
sqequalSqle,
lambdaFormation_alt,
inhabitedIsType,
independent_isectElimination,
voidElimination,
isect_memberEquality_alt,
baseClosed,
isectElimination,
equalitySymmetry,
equalityTransitivity,
sqequalHypSubstitution,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
instantiate,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
introduction
Latex:
\mforall{}k:\mBbbN{}. \mforall{}c,d:\mBbbQ{}Cube(k). Dec(c \mleq{} d)
Date html generated:
2019_10_29-AM-07_49_58
Last ObjectModification:
2019_10_19-AM-10_43_31
Theory : rationals
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