Nuprl Lemma : subtract-wf-partial
∀[x,y:partial(Base)]. (x - y ∈ partial(ℤ))
Proof
Definitions occuring in Statement :
partial: partial(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtract: n - m,
int: ℤ,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
subtract: n - m,
has-value: (a)↓,
and: P ∧ Q,
uiff: uiff(P;Q),
prop: ℙ,
not: ¬A,
implies: P ⇒ Q,
false: False,
squash: ↓T
Lemmas referenced :
partial-not-exception,
base_wf,
partial_wf,
is-exception_wf,
minus-is-int-iff,
subtract_wf,
int-value-type,
base-member-partial,
partial-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
independent_isectElimination,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
because_Cache,
callbyvalueAdd,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
isect_memberEquality,
addExceptionCases,
minusExceptionCases,
independent_functionElimination,
voidElimination,
imageElimination,
imageMemberEquality
Latex:
\mforall{}[x,y:partial(Base)]. (x - y \mmember{} partial(\mBbbZ{}))
Date html generated:
2016_05_14-AM-06_10_27
Last ObjectModification:
2016_01_14-PM-07_50_16
Theory : partial_1
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