Nuprl Lemma : is-rat-cube-face_wf
∀k:ℕ. ∀c,d:ℚCube(k). (is-rat-cube-face(k;c;d) ∈ 𝔹)
Proof
Definitions occuring in Statement :
is-rat-cube-face: is-rat-cube-face(k;c;d),
rational-cube: ℚCube(k),
nat: ℕ,
bool: 𝔹,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
isl: isl(x),
or: P ∨ Q,
decidable: Dec(P),
implies: P ⇒ Q,
is-rat-cube-face: is-rat-cube-face(k;c;d),
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
istype-nat,
rational-cube_wf,
bfalse_wf,
btrue_wf,
rat-cube-face-decider_wf
Rules used in proof :
isectElimination,
universeIsType,
independent_functionElimination,
equalitySymmetry,
equalityTransitivity,
equalityIstype,
unionElimination,
inhabitedIsType,
hypothesis,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
sqequalRule,
cut,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}k:\mBbbN{}. \mforall{}c,d:\mBbbQ{}Cube(k). (is-rat-cube-face(k;c;d) \mmember{} \mBbbB{})
Date html generated:
2019_10_29-AM-07_50_16
Last ObjectModification:
2019_10_19-AM-10_47_49
Theory : rationals
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