`∀[T:Type]. ∀[n:ℕ]. ∀[s:ℕn ⟶ T]. ∀[t:T].  (s++t ∈ ℕn + 1 ⟶ T)`

Proof

Definitions occuring in Statement :  seq-adjoin: `s++t` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` add: `n + m` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` seq-adjoin: `s++t` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ`
Lemmas referenced :  seq-append_wf false_wf le_wf int_seg_wf nat_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality dependent_set_memberEquality natural_numberEquality independent_pairFormation lambdaFormation hypothesis lambdaEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache functionEquality setElimination rename universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[s:\mBbbN{}n  {}\mrightarrow{}  T].  \mforall{}[t:T].    (s++t  \mmember{}  \mBbbN{}n  +  1  {}\mrightarrow{}  T)

Date html generated: 2016_05_13-PM-03_49_16
Last ObjectModification: 2015_12_26-AM-10_17_53

Theory : bar-induction

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