Nuprl Lemma : bdd-diff_weakening
∀a,b:ℕ+ ⟶ ℤ. ((a = b ∈ (ℕ+ ⟶ ℤ)) ⇒ bdd-diff(a;b))
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,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
guard: {T},
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y])
Lemmas referenced :
bdd-diff-equiv,
equal_wf,
nat_plus_wf,
and_wf,
bdd-diff_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
intEquality,
functionExtensionality,
applyEquality,
hypothesisEquality,
productElimination,
dependent_functionElimination,
hyp_replacement,
equalitySymmetry,
sqequalRule,
dependent_set_memberEquality,
independent_pairFormation,
lambdaEquality,
setElimination,
rename,
setEquality
Latex:
\mforall{}a,b:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}. ((a = b) {}\mRightarrow{} bdd-diff(a;b))
Date html generated:
2016_10_26-AM-09_02_40
Last ObjectModification:
2016_07_12-AM-08_12_39
Theory : reals
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