### Nuprl Lemma : rel_exp-one-one

`∀[B:Type]. ∀[R:B ⟶ B ⟶ ℙ].  ∀[n:ℕ]. one-one(B;B;R^n) supposing one-one(B;B;R)`

Proof

Definitions occuring in Statement :  one-one: `one-one(A;B;R)` rel_exp: `R^n` nat: `ℕ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` prop: `ℙ` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` all: `∀x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ` one-one: `one-one(A;B;R)` subtype_rel: `A ⊆r B` rel_exp: `R^n` eq_int: `(i =z j)` subtract: `n - m` ifthenelse: `if b then t else f fi ` btrue: `tt` decidable: `Dec(P)` or: `P ∨ Q` so_lambda: `λ2x.t[x]` so_apply: `x[s]` bool: `𝔹` unit: `Unit` it: `⋅` uiff: `uiff(P;Q)` bfalse: `ff` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` infix_ap: `x f y`
Lemmas referenced :  nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_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 ge_wf less_than_wf rel_exp_wf equal_wf le_wf decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma nat_wf one-one_wf eq_int_wf bool_wf equal-wf-base int_subtype_base assert_wf bnot_wf not_wf exists_wf infix_ap_wf uiff_transitivity eqtt_to_assert assert_of_eq_int iff_transitivity iff_weakening_uiff eqff_to_assert assert_of_bnot
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename intWeakElimination lambdaFormation natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll independent_functionElimination axiomEquality applyEquality cumulativity functionExtensionality because_Cache equalityTransitivity equalitySymmetry dependent_set_memberEquality unionElimination functionEquality universeEquality baseApply closedConclusion baseClosed productElimination productEquality instantiate equalityElimination impliesFunctionality hyp_replacement applyLambdaEquality

Latex:
\mforall{}[B:Type].  \mforall{}[R:B  {}\mrightarrow{}  B  {}\mrightarrow{}  \mBbbP{}].    \mforall{}[n:\mBbbN{}].  one-one(B;B;rel\_exp(B;  R;  n))  supposing  one-one(B;B;R)

Date html generated: 2017_04_17-AM-09_28_09
Last ObjectModification: 2017_02_27-PM-05_29_02

Theory : relations2

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