Nuprl Lemma : uniform-TI-less
∀[P:ℕ ⟶ ℙ]. uniform-TI(ℕ;x,y.y < x;x.P[x])
Proof
Definitions occuring in Statement :
uniform-TI: uniform-TI(T;x,y.R[x; y];t.Q[t]),
nat: ℕ,
less_than: a < b,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uniform-TI: uniform-TI(T;x,y.R[x; y];t.Q[t]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
less_than': less_than'(a;b),
false: False,
not: ¬A
Lemmas referenced :
uniform-comp-nat-induction,
lelt_wf,
nat_wf,
less_than_wf,
uall_wf,
int_seg_wf,
int_seg_subtype_nat,
false_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaFormation,
independent_functionElimination,
setElimination,
rename,
dependent_set_memberEquality,
independent_pairFormation,
productElimination,
setEquality,
natural_numberEquality,
lambdaEquality,
applyEquality,
independent_isectElimination,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[P:\mBbbN{} {}\mrightarrow{} \mBbbP{}]. uniform-TI(\mBbbN{};x,y.y < x;x.P[x])
Date html generated:
2016_05_13-PM-04_03_26
Last ObjectModification:
2015_12_26-AM-10_56_02
Theory : int_1
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