Nuprl Lemma : eq_int_eq_true
∀[i,j:ℤ]. (i =z j) = tt supposing i = j ∈ ℤ
Proof
Definitions occuring in Statement :
eq_int: (i =z j),
btrue: tt,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
true: True
Lemmas referenced :
iff_imp_equal_bool,
eq_int_wf,
btrue_wf,
iff_functionality_wrt_iff,
assert_wf,
equal-wf-base,
int_subtype_base,
true_wf,
iff_weakening_uiff,
assert_of_eq_int,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
intEquality,
applyEquality,
sqequalRule,
independent_functionElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_pairFormation,
lambdaFormation,
natural_numberEquality,
Error :universeIsType,
isect_memberEquality,
axiomEquality,
Error :inhabitedIsType
Latex:
\mforall{}[i,j:\mBbbZ{}]. (i =\msubz{} j) = tt supposing i = j
Date html generated:
2019_06_20-AM-11_31_46
Last ObjectModification:
2018_09_26-AM-11_24_52
Theory : bool_1
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