Nuprl Lemma : nat-deq-aux
∀[a,b:ℕ]. uiff(a = b ∈ ℕ;↑(a =z b))
Proof
Definitions occuring in Statement :
nat: ℕ,
assert: ↑b,
eq_int: (i =z j),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
nat: ℕ,
squash: ↓T,
member: t ∈ T,
le: A ≤ B,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
iff: P ⇐⇒ Q
Lemmas referenced :
equal_wf,
nat_wf,
le_wf,
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,
sqequalHypSubstitution,
applyLambdaEquality,
setElimination,
thin,
rename,
hypothesis,
sqequalRule,
imageMemberEquality,
hypothesisEquality,
baseClosed,
introduction,
productElimination,
extract_by_obid,
isectElimination,
dependent_set_memberEquality,
natural_numberEquality,
intEquality,
addLevel,
independent_isectElimination,
because_Cache,
independent_functionElimination,
cumulativity,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
axiomEquality
Latex:
\mforall{}[a,b:\mBbbN{}]. uiff(a = b;\muparrow{}(a =\msubz{} b))
Date html generated:
2019_06_20-PM-00_31_54
Last ObjectModification:
2018_08_24-PM-10_58_43
Theory : equality!deciders
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