Nuprl Lemma : num-eq-constraints_wf
∀[p:IntConstraints]. (num-eq-constraints(p) ∈ ℕ)
Proof
Definitions occuring in Statement :
num-eq-constraints: num-eq-constraints(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),
num-eq-constraints: num-eq-constraints(p),
pi1: fst(t),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nat: ℕ,
prop: ℙ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q
Lemmas referenced :
int-constraint-problem_wf,
length_wf_nat,
list_wf,
equal-wf-base-T,
list_subtype_base,
int_subtype_base,
false_wf,
le_wf
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,
setEquality,
intEquality,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
independent_isectElimination,
addEquality,
setElimination,
rename,
natural_numberEquality,
dependent_set_memberEquality,
independent_pairFormation,
lambdaFormation
Latex:
\mforall{}[p:IntConstraints]. (num-eq-constraints(p) \mmember{} \mBbbN{})
Date html generated:
2017_04_14-AM-09_10_41
Last ObjectModification:
2017_02_27-PM-03_47_41
Theory : omega
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