Nuprl Lemma : is-above-int
∀[n:ℤ]. ∀[z:Base]. z = n ∈ ℤ supposing is-above(ℤ;n;z)
Proof
Definitions occuring in Statement :
is-above: is-above(T;a;z),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
base: Base,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
is-above: is-above(T;a;z),
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
subtype_rel: A ⊆r B
Lemmas referenced :
is-above_wf,
base_wf,
int_is_mono,
subtype_base_sq,
int_subtype_base,
has-value_wf_base,
is-exception_wf,
and_wf,
equal_wf,
sqle_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
extract_by_obid,
isectElimination,
intEquality,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
sqequalSqle,
divergentSqle,
instantiate,
cumulativity,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
applyEquality,
hyp_replacement,
dependent_set_memberEquality,
independent_pairFormation,
lambdaEquality,
setElimination,
rename,
setEquality
Latex:
\mforall{}[n:\mBbbZ{}]. \mforall{}[z:Base]. z = n supposing is-above(\mBbbZ{};n;z)
Date html generated:
2016_10_21-AM-09_41_33
Last ObjectModification:
2016_07_12-AM-05_03_38
Theory : subtype_1
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