Nuprl Lemma : rat-cube-face_wf
∀[k:ℕ]. ∀[c,d:ℚCube(k)]. (c ≤ d ∈ ℙ)
Proof
Definitions occuring in Statement :
rat-cube-face: c ≤ d,
rational-cube: ℚCube(k),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
rational-cube: ℚCube(k),
nat: ℕ,
all: ∀x:A. B[x],
prop: ℙ,
rat-cube-face: c ≤ d,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
rational-cube_wf,
rat-interval-face_wf,
int_seg_wf
Rules used in proof :
universeIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
inhabitedIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
hypothesis,
hypothesisEquality,
rename,
setElimination,
natural_numberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
functionEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[c,d:\mBbbQ{}Cube(k)]. (c \mleq{} d \mmember{} \mBbbP{})
Date html generated:
2019_10_29-AM-07_49_33
Last ObjectModification:
2019_10_17-PM-01_29_14
Theory : rationals
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