Nuprl Lemma : int-between
∀i,j:ℤ. ∃k:ℤ. ((i ≤ k) ∧ k < j) supposing i < j
Proof
Definitions occuring in Statement :
less_than: a < b,
uimplies: b supposing a,
le: A ≤ B,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
member-less_than,
le_weakening,
and_wf,
le_wf,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
rename,
dependent_pairFormation,
because_Cache,
independent_pairFormation,
dependent_functionElimination,
intEquality
Latex:
\mforall{}i,j:\mBbbZ{}. \mexists{}k:\mBbbZ{}. ((i \mleq{} k) \mwedge{} k < j) supposing i < j
Date html generated:
2019_06_20-PM-02_37_37
Last ObjectModification:
2019_06_12-PM-00_26_16
Theory : num_thy_1
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