Nuprl Lemma : compatible-rat-cubes-symm
∀[k:ℕ]. ∀[c,d:ℚCube(k)]. (Compatible(c;d) ⇒ 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],
implies: P ⇒ Q
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
guard: {T},
true: True,
prop: ℙ,
squash: ↓T,
uimplies: b supposing a,
member: t ∈ T,
cand: A c∧ B,
and: P ∧ Q,
compatible-rat-cubes: Compatible(c;d),
implies: P ⇒ Q,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
rational-cube_wf,
compatible-rat-cubes_wf,
iff_weakening_equal,
subtype_rel_self,
rat-cube-face_wf,
rat-cube-intersection-symm,
true_wf,
squash_wf,
assert_functionality_wrt_uiff,
assert_wf,
iff_weakening_uiff,
rat-cube-intersection_wf,
inhabited-rat-cube_wf,
istype-assert
Rules used in proof :
inhabitedIsType,
promote_hyp,
universeEquality,
instantiate,
baseClosed,
imageMemberEquality,
sqequalRule,
natural_numberEquality,
universeIsType,
equalitySymmetry,
equalityTransitivity,
imageElimination,
lambdaEquality_alt,
applyEquality,
independent_isectElimination,
because_Cache,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
independent_pairFormation,
productElimination,
hypothesis,
thin,
independent_functionElimination,
cut,
sqequalHypSubstitution,
lambdaFormation_alt,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[c,d:\mBbbQ{}Cube(k)]. (Compatible(c;d) {}\mRightarrow{} Compatible(d;c))
Date html generated:
2019_10_29-AM-07_54_15
Last ObjectModification:
2019_10_18-PM-00_51_27
Theory : rationals
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