Nuprl Lemma : assert-int-deq
∀[x,y:ℤ]. uiff(↑(IntDeq x y);x = y ∈ ℤ)
Proof
Definitions occuring in Statement :
int-deq: IntDeq,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
apply: f a,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int-deq: IntDeq,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
deq: EqDecider(T)
Lemmas referenced :
equal-wf-base,
int_subtype_base,
iff_weakening_uiff,
assert_wf,
eq_int_wf,
assert_of_eq_int,
assert_witness,
uiff_wf,
int-deq_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
independent_pairFormation,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
applyEquality,
because_Cache,
addLevel,
productElimination,
independent_isectElimination,
independent_functionElimination,
cumulativity,
instantiate,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
lambdaEquality,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x,y:\mBbbZ{}]. uiff(\muparrow{}(IntDeq x y);x = y)
Date html generated:
2019_06_20-PM-00_31_56
Last ObjectModification:
2018_08_24-PM-10_58_42
Theory : equality!deciders
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