Nuprl Lemma : le_int-wf-partial2
∀[x,y:partial(ℤ)]. (x ≤z y ∈ partial(𝔹))
Proof
Definitions occuring in Statement :
partial: partial(T),
le_int: i ≤z j,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a
Lemmas referenced :
le_int-wf-partial,
subtype_rel_partial,
base_wf,
int_subtype_base,
partial_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
intEquality,
hypothesis,
independent_isectElimination,
sqequalRule,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[x,y:partial(\mBbbZ{})]. (x \mleq{}z y \mmember{} partial(\mBbbB{}))
Date html generated:
2016_05_14-AM-06_10_36
Last ObjectModification:
2015_12_26-AM-11_51_46
Theory : partial_1
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