### Nuprl Lemma : init-seg-nat-seq_wf

`∀[f,g:finite-nat-seq()].  (init-seg-nat-seq(f;g) ∈ 𝔹)`

Proof

Definitions occuring in Statement :  init-seg-nat-seq: `init-seg-nat-seq(f;g)` finite-nat-seq: `finite-nat-seq()` bool: `𝔹` uall: `∀[x:A]. B[x]` member: `t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` init-seg-nat-seq: `init-seg-nat-seq(f;g)` finite-nat-seq: `finite-nat-seq()` nat: `ℕ` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` bfalse: `ff` prop: `ℙ` iff: `P `⇐⇒` Q` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A`
Lemmas referenced :  ble_wf bool_wf eqtt_to_assert equal-upto-finite-nat-seq_wf int_seg_wf equal_wf finite-nat-seq_wf assert-ble subtype_rel_dep_function nat_wf int_seg_subtype false_wf subtype_rel_self
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule sqequalHypSubstitution productElimination thin extract_by_obid isectElimination setElimination rename hypothesisEquality hypothesis lambdaFormation unionElimination equalityElimination independent_isectElimination functionExtensionality applyEquality natural_numberEquality because_Cache equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination axiomEquality isect_memberEquality lambdaEquality independent_pairFormation

Latex:
\mforall{}[f,g:finite-nat-seq()].    (init-seg-nat-seq(f;g)  \mmember{}  \mBbbB{})

Date html generated: 2017_04_20-AM-07_29_29
Last ObjectModification: 2017_02_27-PM-06_00_29

Theory : continuity

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