Nuprl Lemma : not-canonicalizable-baire-to-nat
¬⇃(canonicalizable((ℕ ⟶ ℕ) ⟶ ℕ))
Proof
Definitions occuring in Statement :
quotient: x,y:A//B[x; y],
canonicalizable: canonicalizable(T),
nat: ℕ,
not: ¬A,
true: True,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
not: ¬A,
all: ∀x:A. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
subtype_rel: A ⊆r B
Lemmas referenced :
choice-principle_wf,
not_wf,
equiv_rel_true,
true_wf,
canonicalizable_wf,
quotient_wf,
nat_wf,
choice-iff-canonicalizable,
not-choice-baire-to-nat
Rules used in proof :
cut,
lemma_by_obid,
hypothesis,
addLevel,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
impliesFunctionality,
dependent_functionElimination,
thin,
functionEquality,
productElimination,
independent_pairFormation,
independent_functionElimination,
isectElimination,
because_Cache,
sqequalRule,
lambdaEquality,
independent_isectElimination,
applyEquality,
cumulativity,
hypothesisEquality,
universeEquality,
instantiate
Latex:
\mneg{}\00D9(canonicalizable((\mBbbN{} {}\mrightarrow{} \mBbbN{}) {}\mrightarrow{} \mBbbN{}))
Date html generated:
2016_05_14-PM-09_42_41
Last ObjectModification:
2016_01_13-AM-10_27_17
Theory : continuity
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