Nuprl Lemma : rminus_functionality_wrt_bdd-diff
∀x,y:ℕ+ ⟶ ℤ. (bdd-diff(x;y) ⇒ bdd-diff(-(x);-(y)))
Proof
Definitions occuring in Statement :
rminus: -(x),
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 :
all: ∀x:A. B[x],
implies: P ⇒ Q,
rminus: -(x),
bdd-diff: bdd-diff(f;g),
exists: ∃x:A. B[x],
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
nat: ℕ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
subtract: n - m,
top: Top
Lemmas referenced :
le_wf,
squash_wf,
true_wf,
istype-int,
absval_sym,
subtract_wf,
subtype_rel_self,
iff_weakening_equal,
minus-minus,
minus-add,
istype-void,
minus-one-mul,
nat_plus_wf,
istype-le,
absval_wf,
bdd-diff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation_alt,
hypothesisEquality,
cut,
hypothesis,
dependent_functionElimination,
sqequalRule,
applyEquality,
lambdaEquality_alt,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
equalityTransitivity,
equalitySymmetry,
universeIsType,
inhabitedIsType,
minusEquality,
setElimination,
rename,
natural_numberEquality,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality,
independent_isectElimination,
independent_functionElimination,
isect_memberEquality_alt,
voidElimination,
because_Cache,
functionIsType
Latex:
\mforall{}x,y:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}. (bdd-diff(x;y) {}\mRightarrow{} bdd-diff(-(x);-(y)))
Date html generated:
2019_10_16-PM-03_07_11
Last ObjectModification:
2018_11_08-PM-05_56_56
Theory : reals
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