### Nuprl Lemma : causal_order_reflexive

`∀[T:Type]. ∀L:T List. ∀[R:ℕ||L|| ⟶ ℕ||L|| ⟶ ℙ]. ∀[P:ℕ||L|| ⟶ ℙ].  (Refl(ℕ||L||)(R _1 _2) `` causal_order(L;R;P;P))`

Proof

Definitions occuring in Statement :  causal_order: `causal_order(L;R;P;Q)` length: `||as||` list: `T List` refl: `Refl(T;x,y.E[x; y])` int_seg: `{i..j-}` uall: `∀[x:A]. B[x]` prop: `ℙ` all: `∀x:A. B[x]` implies: `P `` Q` apply: `f a` function: `x:A ⟶ B[x]` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  causal_order: `causal_order(L;R;P;Q)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` exists: `∃x:A. B[x]` member: `t ∈ T` and: `P ∧ Q` cand: `A c∧ B` guard: `{T}` int_seg: `{i..j-}` lelt: `i ≤ j < k` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` false: `False` top: `Top` prop: `ℙ` subtype_rel: `A ⊆r B` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` refl: `Refl(T;x,y.E[x; y])`
Lemmas referenced :  int_seg_properties length_wf decidable__le full-omega-unsat intformnot_wf intformle_wf itermVar_wf int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_var_lemma int_formula_prop_wf le_wf subtype_rel_self int_seg_wf refl_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation_alt lambdaFormation dependent_pairFormation hypothesisEquality cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality hypothesis setElimination rename productElimination dependent_functionElimination because_Cache unionElimination independent_isectElimination approximateComputation independent_functionElimination lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation productEquality applyEquality instantiate universeEquality functionIsType universeIsType inhabitedIsType

Latex:
\mforall{}[T:Type]
\mforall{}L:T  List
\mforall{}[R:\mBbbN{}||L||  {}\mrightarrow{}  \mBbbN{}||L||  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[P:\mBbbN{}||L||  {}\mrightarrow{}  \mBbbP{}].    (Refl(\mBbbN{}||L||)(R  \$_{1}\$  \$\mbackslash{}\000Cff5f{2}\$)  {}\mRightarrow{}  causal\_order(L;R;P;P))

Date html generated: 2019_10_15-AM-10_57_34
Last ObjectModification: 2018_09_27-AM-09_52_41

Theory : list!

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