Nuprl Lemma : int-problem-dimension_wf
∀[p:IntConstraints]. (dim(p) ∈ ℕ)
Proof
Definitions occuring in Statement :
int-problem-dimension: dim(p),
int-constraint-problem: IntConstraints,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int-constraint-problem: IntConstraints,
tunion: ⋃x:A.B[x],
pi2: snd(t),
so_lambda: λ2x.t[x],
nat: ℕ,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
or: P ∨ Q,
cons: [a / b],
int-problem-dimension: dim(p),
nil: [],
it: ⋅,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
top: Top,
decidable: Dec(P),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
sq_stable: SqStable(P),
squash: ↓T,
guard: {T},
subtract: n - m,
subtype_rel: A ⊆r B,
true: True
Lemmas referenced :
int-constraint-problem_wf,
set_wf,
list_wf,
equal_wf,
length_wf,
list-cases,
product_subtype_list,
false_wf,
le_wf,
reduce_hd_cons_lemma,
subtract_wf,
decidable__le,
not-le-2,
sq_stable__le,
le_antisymmetry_iff,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-commutes,
zero-add,
minus-minus,
add-associates,
add_functionality_wrt_le,
add-zero,
le-add-cancel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
unionElimination,
thin,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
imageElimination,
productElimination,
isectElimination,
intEquality,
lambdaEquality,
hypothesisEquality,
addEquality,
setElimination,
rename,
natural_numberEquality,
dependent_functionElimination,
promote_hyp,
hypothesis_subsumption,
dependent_set_memberEquality,
independent_pairFormation,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
independent_functionElimination,
independent_isectElimination,
imageMemberEquality,
baseClosed,
applyEquality,
because_Cache,
minusEquality
Latex:
\mforall{}[p:IntConstraints]. (dim(p) \mmember{} \mBbbN{})
Date html generated:
2017_04_14-AM-09_10_37
Last ObjectModification:
2017_02_27-PM-03_47_44
Theory : omega
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