Nuprl Lemma : eq_int_eq_false_elim_sqequal
∀[i,j:ℤ]. i ≠ j supposing (i =z j) ~ ff
Proof
Definitions occuring in Statement :
eq_int: (i =z j),
bfalse: ff,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
nequal: a ≠ b ∈ T ,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
false: False,
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
assert_of_ff,
neg_assert_of_eq_int,
equal-wf-base,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
productElimination,
independent_isectElimination,
independent_functionElimination,
voidElimination,
intEquality,
applyEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
baseClosed,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[i,j:\mBbbZ{}]. i \mneq{} j supposing (i =\msubz{} j) \msim{} ff
Date html generated:
2017_04_14-AM-07_36_36
Last ObjectModification:
2017_02_27-PM-03_08_43
Theory : subtype_1
Home
Index