Nuprl Lemma : compatible-rat-cubes-refl
∀[k:ℕ]. ∀[c:ℚCube(k)]. ∀d:ℚCube(k). ((c = d ∈ ℚCube(k)) ⇒ Compatible(d;c))
Proof
Definitions occuring in Statement :
compatible-rat-cubes: Compatible(c;d),
rational-cube: ℚCube(k),
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
guard: {T},
uimplies: b supposing a,
subtype_rel: A ⊆r B,
squash: ↓T,
true: True,
member: t ∈ T,
prop: ℙ,
cand: A c∧ B,
and: P ∧ Q,
compatible-rat-cubes: Compatible(c;d),
implies: P ⇒ Q,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x]
Lemmas referenced :
subtype_rel_self,
true_wf,
squash_wf,
rat-cube-face-self,
iff_weakening_equal,
rat-cube-intersection-idemp,
istype-nat,
rational-cube_wf,
inhabited-rat-cube_wf,
istype-assert,
rat-cube-intersection_wf,
rat-cube-face_wf
Rules used in proof :
universeEquality,
instantiate,
dependent_functionElimination,
independent_functionElimination,
independent_isectElimination,
baseClosed,
imageMemberEquality,
because_Cache,
imageElimination,
lambdaEquality_alt,
applyEquality,
natural_numberEquality,
universeIsType,
isectElimination,
extract_by_obid,
introduction,
productElimination,
sqequalHypSubstitution,
rename,
setElimination,
applyLambdaEquality,
hypothesisEquality,
inhabitedIsType,
equalityIstype,
productIsType,
equalityTransitivity,
dependent_set_memberEquality_alt,
sqequalRule,
equalitySymmetry,
thin,
hyp_replacement,
hypothesis,
independent_pairFormation,
cut,
lambdaFormation_alt,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[c:\mBbbQ{}Cube(k)]. \mforall{}d:\mBbbQ{}Cube(k). ((c = d) {}\mRightarrow{} Compatible(d;c))
Date html generated:
2019_10_29-AM-07_54_21
Last ObjectModification:
2019_10_18-PM-01_04_17
Theory : rationals
Home
Index