Nuprl Lemma : int_entire_a
∀[a,b:ℤ]. (a * b ≠ 0) supposing (b ≠ 0 and a ≠ 0)
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
nequal: a ≠ b ∈ T ,
multiply: n * m,
natural_number: $n,
int: ℤ
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,
prop: ℙ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
subtract: n - m,
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
equal-wf-base,
int_subtype_base,
nequal_wf,
decidable__int_equal,
int_entire,
subtract_wf,
minus-zero,
zero-add,
add-zero,
subtype_base_sq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
hypothesis,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
intEquality,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
because_Cache,
lambdaEquality,
dependent_functionElimination,
natural_numberEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
multiplyEquality,
unionElimination,
independent_isectElimination,
addEquality,
instantiate,
cumulativity
Latex:
\mforall{}[a,b:\mBbbZ{}]. (a * b \mneq{} 0) supposing (b \mneq{} 0 and a \mneq{} 0)
Date html generated:
2017_04_14-AM-07_20_33
Last ObjectModification:
2017_02_27-PM-02_53_46
Theory : arithmetic
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