### Nuprl Lemma : seq-append0-left

`∀[t:Top]. ∀[m:ℕ]. ∀[f:ℕm ⟶ ℕ].  (seq-append(0;m;t;f) = f ∈ (ℕm ⟶ ℕ))`

Proof

Definitions occuring in Statement :  seq-append: `seq-append(n;m;s1;s2)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` top: `Top` function: `x:A ⟶ B[x]` natural_number: `\$n` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` seq-append: `seq-append(n;m;s1;s2)` int_seg: `{i..j-}` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` less_than: `a < b` less_than': `less_than'(a;b)` top: `Top` true: `True` squash: `↓T` not: `¬A` false: `False` prop: `ℙ` guard: `{T}` nat: `ℕ` ge: `i ≥ j ` lelt: `i ≤ j < k` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` le: `A ≤ B` subtype_rel: `A ⊆r B` decidable: `Dec(P)` or: `P ∨ Q` bfalse: `ff` sq_type: `SQType(T)` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` subtract: `n - m`
Lemmas referenced :  lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int top_wf less_than_wf int_seg_properties nat_properties decidable__equal_int satisfiable-full-omega-tt intformand_wf intformless_wf itermVar_wf itermConstant_wf intformle_wf int_formula_prop_and_lemma int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_wf int_seg_wf lelt_wf le_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot minus-zero add-zero intformnot_wf itermAdd_wf int_formula_prop_not_lemma int_term_value_add_lemma nat_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut functionExtensionality sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis natural_numberEquality lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination because_Cache lessCases sqequalAxiom isect_memberEquality independent_pairFormation voidElimination voidEquality imageMemberEquality baseClosed imageElimination independent_functionElimination dependent_functionElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality computeAll applyEquality dependent_set_memberEquality promote_hyp instantiate cumulativity addEquality functionEquality axiomEquality

Latex:
\mforall{}[t:Top].  \mforall{}[m:\mBbbN{}].  \mforall{}[f:\mBbbN{}m  {}\mrightarrow{}  \mBbbN{}].    (seq-append(0;m;t;f)  =  f)

Date html generated: 2017_04_17-AM-10_02_51
Last ObjectModification: 2017_02_27-PM-05_54_24

Theory : continuity

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