Nuprl Lemma : bdd-diff_transitivity
∀a,b,c:ℕ+ ⟶ ℤ. (bdd-diff(a;b) ⇒ bdd-diff(b;c) ⇒ bdd-diff(a;c))
Proof
Definitions occuring in Statement :
bdd-diff: bdd-diff(f;g),
nat_plus: ℕ+,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
guard: {T},
trans: Trans(T;x,y.E[x; y])
Lemmas referenced :
bdd-diff-equiv,
bdd-diff_wf,
nat_plus_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
productElimination,
thin,
lambdaFormation,
isectElimination,
hypothesisEquality,
hypothesis,
functionEquality,
intEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}a,b,c:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}. (bdd-diff(a;b) {}\mRightarrow{} bdd-diff(b;c) {}\mRightarrow{} bdd-diff(a;c))
Date html generated:
2016_05_18-AM-06_46_29
Last ObjectModification:
2015_12_28-AM-00_24_47
Theory : reals
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