Nuprl Lemma : bdd-diff_functionality
∀x1,x2,y1,y2:ℕ+ ⟶ ℤ. (bdd-diff(x1;x2) ⇒ bdd-diff(y1;y2) ⇒ (bdd-diff(x1;y1) ⇐⇒ bdd-diff(x2;y2)))
Proof
Definitions occuring in Statement :
bdd-diff: bdd-diff(f;g),
nat_plus: ℕ+,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
equiv_rel: EquivRel(T;x,y.E[x; y]),
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
trans: Trans(T;x,y.E[x; y]),
guard: {T},
sym: Sym(T;x,y.E[x; y])
Lemmas referenced :
bdd-diff-equiv,
bdd-diff_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
productElimination,
thin,
isectElimination,
hypothesisEquality,
hypothesis,
functionEquality,
intEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}x1,x2,y1,y2:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}. (bdd-diff(x1;x2) {}\mRightarrow{} bdd-diff(y1;y2) {}\mRightarrow{} (bdd-diff(x1;y1) \mLeftarrow{}{}\mRightarrow{} bdd-diff(x2;y2)))
Date html generated:
2016_05_18-AM-06_46_32
Last ObjectModification:
2015_12_28-AM-00_24_51
Theory : reals
Home
Index