Nuprl Lemma : mul_bounds_1a
∀[a,b:ℕ]. (0 ≤ (a * b))
Proof
Definitions occuring in Statement :
nat: ℕ,
uall: ∀[x:A]. B[x],
le: A ≤ B,
multiply: n * m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
nat: ℕ,
prop: ℙ,
squash: ↓T,
sq_stable: SqStable(P),
uimplies: b supposing a,
top: Top,
uiff: uiff(P;Q),
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B
Lemmas referenced :
less_than'_wf,
nat_wf,
multiply-is-int-iff,
set_subtype_base,
le_wf,
int_subtype_base,
mul-commutes,
zero-mul,
mul_preserves_le,
sq_stable__le
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
because_Cache,
extract_by_obid,
isectElimination,
multiplyEquality,
setElimination,
rename,
hypothesis,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
isect_memberEquality,
voidElimination,
Error :universeIsType,
imageElimination,
baseClosed,
imageMemberEquality,
independent_functionElimination,
independent_isectElimination,
lemma_by_obid,
voidEquality,
intEquality,
applyEquality,
closedConclusion,
baseApply
Latex:
\mforall{}[a,b:\mBbbN{}]. (0 \mleq{} (a * b))
Date html generated:
2019_06_20-AM-11_26_39
Last ObjectModification:
2018_09_26-AM-10_58_35
Theory : arithmetic
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