Nuprl Lemma : change-from1_wf
∀[a:ℕ ⟶ ℕ]. (change-from1(a) ∈ ℕ ⟶ 𝔹)
Proof
Definitions occuring in Statement :
change-from1: change-from1(a),
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
prop: ℙ,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
nat: ℕ,
change-from1: change-from1(a),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
btrue_wf,
le_wf,
false_wf,
nat_wf,
bfalse_wf
Rules used in proof :
functionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
isectElimination,
lambdaFormation,
independent_pairFormation,
dependent_set_memberEquality,
hypothesisEquality,
functionExtensionality,
applyEquality,
extract_by_obid,
natural_numberEquality,
hypothesis,
because_Cache,
rename,
thin,
setElimination,
sqequalHypSubstitution,
int_eqEquality,
lambdaEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. (change-from1(a) \mmember{} \mBbbN{} {}\mrightarrow{} \mBbbB{})
Date html generated:
2017_04_21-AM-11_23_23
Last ObjectModification:
2017_04_20-PM-04_55_51
Theory : continuity
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