Nuprl Lemma : evodd-succ_wf
∀[b:𝔹]. ∀[n:pw-evenodd() (¬bb)]. (evodd-succ(n) ∈ pw-evenodd() b)
Proof
Definitions occuring in Statement :
evodd-succ: evodd-succ(n),
pw-evenodd: pw-evenodd(),
bnot: ¬bb,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a
Definitions unfolded in proof :
pw-evenodd: pw-evenodd(),
uall: ∀[x:A]. B[x],
member: t ∈ T,
evodd-succ: evodd-succ(n),
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
unit: Unit,
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
pW-sup_wf,
bool_wf,
equal-wf-T-base,
unit_wf2,
bnot_wf,
param-W_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
unionEquality,
because_Cache,
unionElimination,
voidEquality,
hypothesisEquality,
inrEquality,
axiomEquality,
natural_numberEquality,
baseClosed,
instantiate,
equalityTransitivity,
equalitySymmetry,
applyEquality,
lambdaFormation,
dependent_functionElimination,
independent_functionElimination,
isect_memberEquality
Latex:
\mforall{}[b:\mBbbB{}]. \mforall{}[n:pw-evenodd() (\mneg{}\msubb{}b)]. (evodd-succ(n) \mmember{} pw-evenodd() b)
Date html generated:
2019_06_20-PM-00_36_22
Last ObjectModification:
2018_08_21-PM-01_53_42
Theory : co-recursion
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