Nuprl Lemma : add-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,
add: 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,
has-value: (a)↓,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
false: False,
squash: ↓T
Lemmas referenced :
partial-base,
partial_wf,
base_wf,
base-member-partial,
int-value-type,
is-exception_wf,
partial-not-exception
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
hypothesisEquality,
Error :isect_memberEquality_alt,
isectElimination,
thin,
Error :universeIsType,
intEquality,
independent_isectElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
callbyvalueAdd,
productElimination,
addEquality,
because_Cache,
Error :lambdaFormation_alt,
addExceptionCases,
independent_functionElimination,
voidElimination,
imageElimination,
imageMemberEquality
Latex:
\mforall{}[x,y:partial(Base)]. (x + y \mmember{} partial(\mBbbZ{}))
Date html generated:
2019_06_20-PM-00_34_17
Last ObjectModification:
2018_10_06-PM-04_56_22
Theory : partial_1
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