### Nuprl Lemma : firstn-mklist1

`∀[m,n:ℕ]. ∀[f:ℕm ⟶ Top].  ((n ≤ m) `` (firstn(n;mklist(m;f)) ~ mklist(n;f)))`

Proof

Definitions occuring in Statement :  mklist: `mklist(n;f)` firstn: `firstn(n;as)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` top: `Top` le: `A ≤ B` implies: `P `` Q` function: `x:A ⟶ B[x]` natural_number: `\$n` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` implies: `P `` Q` prop: `ℙ` nat: `ℕ` uimplies: `b supposing a` sq_type: `SQType(T)` all: `∀x:A. B[x]` guard: `{T}` squash: `↓T` true: `True` subtype_rel: `A ⊆r B` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` bnot: `¬bb` assert: `↑b` false: `False` not: `¬A`
Lemmas referenced :  le_wf int_seg_wf top_wf nat_wf firstn-mklist subtype_base_sq int_subtype_base equal_wf squash_wf true_wf imin_unfold iff_weakening_equal le_int_wf bool_wf eqtt_to_assert assert_of_le_int eqff_to_assert bool_cases_sqequal bool_subtype_base assert-bnot
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaFormation hypothesis extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality sqequalRule lambdaEquality dependent_functionElimination sqequalAxiom because_Cache functionEquality natural_numberEquality isect_memberEquality instantiate cumulativity intEquality independent_isectElimination equalityTransitivity equalitySymmetry independent_functionElimination applyEquality imageElimination universeEquality imageMemberEquality baseClosed productElimination unionElimination equalityElimination dependent_pairFormation promote_hyp voidElimination

Latex:
\mforall{}[m,n:\mBbbN{}].  \mforall{}[f:\mBbbN{}m  {}\mrightarrow{}  Top].    ((n  \mleq{}  m)  {}\mRightarrow{}  (firstn(n;mklist(m;f))  \msim{}  mklist(n;f)))

Date html generated: 2017_04_17-AM-08_01_41
Last ObjectModification: 2017_02_27-PM-04_31_53

Theory : list_1

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