### Nuprl Lemma : fun-path_wf

`∀[T:Type]. ∀[f:T ⟶ T]. ∀[x,y:T]. ∀[L:T List].  (x=f*(y) via L ∈ ℙ)`

Proof

Definitions occuring in Statement :  fun-path: `y=f*(x) via L` list: `T List` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  fun-path: `y=f*(x) via L` uall: `∀[x:A]. B[x]` member: `t ∈ T` prop: `ℙ` and: `P ∧ Q` uimplies: `b supposing a` ge: `i ≥ j ` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` less_than: `a < b` squash: `↓T` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` assert: `↑b` ifthenelse: `if b then t else f fi ` btrue: `tt` less_than': `less_than'(a;b)` cons: `[a / b]` bfalse: `ff` so_lambda: `λ2x.t[x]` int_seg: `{i..j-}` guard: `{T}` lelt: `i ≤ j < k` so_apply: `x[s]`
Lemmas referenced :  less_than_wf length_wf equal_wf hd_wf decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf last_wf list-cases null_nil_lemma length_of_nil_lemma product_subtype_list null_cons_lemma length_of_cons_lemma false_wf all_wf int_seg_wf subtract_wf select_wf int_seg_properties decidable__lt itermSubtract_wf int_term_value_subtract_lemma itermAdd_wf int_term_value_add_lemma not_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut productEquality extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality cumulativity hypothesisEquality hypothesis because_Cache independent_isectElimination dependent_functionElimination unionElimination imageElimination productElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll promote_hyp hypothesis_subsumption lambdaFormation setElimination rename applyEquality functionExtensionality addEquality equalityTransitivity equalitySymmetry axiomEquality functionEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[f:T  {}\mrightarrow{}  T].  \mforall{}[x,y:T].  \mforall{}[L:T  List].    (x=f*(y)  via  L  \mmember{}  \mBbbP{})

Date html generated: 2018_05_21-PM-07_42_51
Last ObjectModification: 2017_07_26-PM-05_20_52

Theory : general

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