Nuprl Lemma : add-wf-bar-int
∀[x,y:bar(ℤ)]. (x + y ∈ bar(ℤ))
Proof
Definitions occuring in Statement :
bar: bar(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
add: n + m,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
guard: {T},
or: P ∨ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
subtype_bar2,
base_wf,
int_subtype_base,
value-type_wf,
subtype_rel_self,
bar-base,
add-wf-bar,
subtype_barSqtype_base,
int-value-type
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesis,
independent_isectElimination,
independent_pairFormation,
sqequalRule,
inrFormation,
because_Cache,
hypothesisEquality,
applyEquality,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[x,y:bar(\mBbbZ{})]. (x + y \mmember{} bar(\mBbbZ{}))
Date html generated:
2016_07_08-PM-05_18_51
Last ObjectModification:
2015_12_27-PM-05_17_13
Theory : bar!type
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