Nuprl Lemma : sq_stable__compatible-rat-cubes
∀k:ℕ. ∀c,d:ℚCube(k). SqStable(Compatible(c;d))
Proof
Definitions occuring in Statement :
compatible-rat-cubes: Compatible(c;d),
rational-cube: ℚCube(k),
nat: ℕ,
sq_stable: SqStable(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
istype-nat,
rational-cube_wf,
decidable__compatible-rat-cubes,
compatible-rat-cubes_wf,
sq_stable_from_decidable
Rules used in proof :
universeIsType,
inhabitedIsType,
dependent_functionElimination,
independent_functionElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}k:\mBbbN{}. \mforall{}c,d:\mBbbQ{}Cube(k). SqStable(Compatible(c;d))
Date html generated:
2019_10_29-AM-07_54_44
Last ObjectModification:
2019_10_17-PM-01_47_10
Theory : rationals
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