Nuprl Lemma : isOdd-2n+1
∀n:ℤ. (isOdd((2 * n) + 1) ~ tt)
Proof
Definitions occuring in Statement :
isOdd: isOdd(n),
btrue: tt,
all: ∀x:A. B[x],
multiply: n * m,
add: n + m,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
isOdd_wf,
assert-isOdd,
int_subtype_base,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesis,
independent_isectElimination,
addEquality,
multiplyEquality,
natural_numberEquality,
hypothesisEquality,
productElimination,
dependent_functionElimination,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :equalityIstype,
Error :inhabitedIsType,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
sqequalBase,
equalitySymmetry,
equalityTransitivity
Latex:
\mforall{}n:\mBbbZ{}. (isOdd((2 * n) + 1) \msim{} tt)
Date html generated:
2019_06_20-PM-02_24_37
Last ObjectModification:
2019_02_01-AM-11_23_05
Theory : num_thy_1
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