Nuprl Lemma : rat-point-in-cube_wf
∀[k:ℕ]. ∀[x:ℕk ⟶ ℚ]. ∀[c:ℚCube(k)]. (rat-point-in-cube(k;x;c) ∈ ℙ)
Proof
Definitions occuring in Statement :
rat-point-in-cube: rat-point-in-cube(k;x;c),
rational-cube: ℚCube(k),
rationals: ℚ,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rat-point-in-cube: rat-point-in-cube(k;x;c),
prop: ℙ,
all: ∀x:A. B[x],
nat: ℕ,
and: P ∧ Q,
rational-cube: ℚCube(k),
implies: P ⇒ Q,
rational-interval: ℚInterval,
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
int_seg_wf,
qle_wf,
rational-cube_wf,
rationals_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
because_Cache,
hypothesis,
productEquality,
applyEquality,
hypothesisEquality,
inhabitedIsType,
lambdaFormation_alt,
productElimination,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
functionIsType
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[x:\mBbbN{}k {}\mrightarrow{} \mBbbQ{}]. \mforall{}[c:\mBbbQ{}Cube(k)]. (rat-point-in-cube(k;x;c) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-09_18_05
Last ObjectModification:
2019_11_02-PM-04_21_53
Theory : rationals
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