Nuprl Lemma : equal-upto-finite-nat-seq_wf
∀[n:ℕ]. ∀[f,g:ℕn ⟶ ℕ]. (equal-upto-finite-nat-seq(n;f;g) ∈ 𝔹)
Proof
Definitions occuring in Statement :
equal-upto-finite-nat-seq: equal-upto-finite-nat-seq(n;f;g),
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
equal-upto-finite-nat-seq: equal-upto-finite-nat-seq(n;f;g),
subtype_rel: A ⊆r B,
nat: ℕ
Lemmas referenced :
nat_wf,
int_seg_wf,
eq_int_wf,
band_wf,
btrue_wf,
bool_wf,
primrec_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
lambdaEquality,
applyEquality,
setElimination,
rename,
because_Cache,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[f,g:\mBbbN{}n {}\mrightarrow{} \mBbbN{}]. (equal-upto-finite-nat-seq(n;f;g) \mmember{} \mBbbB{})
Date html generated:
2016_05_14-PM-09_55_08
Last ObjectModification:
2016_01_15-AM-10_56_52
Theory : continuity
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