Nuprl Lemma : int-deq-aux
∀[a,b:ℤ]. uiff(a = b ∈ ℤ;↑(a =z b))
Proof
Definitions occuring in Statement :
assert: ↑b,
eq_int: (i =z j),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
iff: P ⇐⇒ Q
Lemmas referenced :
equal-wf-base,
int_subtype_base,
iff_weakening_uiff,
assert_wf,
eq_int_wf,
assert_of_eq_int,
assert_witness,
uiff_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
isect_memberFormation,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
applyEquality,
sqequalRule,
because_Cache,
addLevel,
productElimination,
independent_isectElimination,
independent_functionElimination,
instantiate,
cumulativity,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
axiomEquality
Latex:
\mforall{}[a,b:\mBbbZ{}]. uiff(a = b;\muparrow{}(a =\msubz{} b))
Date html generated:
2019_06_20-PM-00_31_55
Last ObjectModification:
2018_08_24-PM-10_58_43
Theory : equality!deciders
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