Nuprl Lemma : int_seg_well_founded_down

`∀i:ℤ. ∀j:{i...}.  WellFnd{i}({i..j-};x,y.x > y)`

Proof

Definitions occuring in Statement :  int_upper: `{i...}` int_seg: `{i..j-}` wellfounded: `WellFnd{i}(A;x,y.R[x; y])` gt: `i > j` all: `∀x:A. B[x]` int: `ℤ`
Definitions unfolded in proof :  all: `∀x:A. B[x]` member: `t ∈ T` uall: `∀[x:A]. B[x]` so_lambda: `λ2x y.t[x; y]` int_upper: `{i...}` so_apply: `x[s1;s2]` int_seg: `{i..j-}` guard: `{T}` lelt: `i ≤ j < k` and: `P ∧ Q` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` not: `¬A` implies: `P `` Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` top: `Top` prop: `ℙ` uiff: `uiff(P;Q)` gt: `i > j` iff: `P `⇐⇒` Q` wellfounded: `WellFnd{i}(A;x,y.R[x; y])` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  int_upper_wf int_upper_well_founded inv_image_ind less_than_wf int_seg_wf subtract_wf int_seg_properties int_upper_properties decidable__le full-omega-unsat intformand_wf intformnot_wf intformle_wf itermConstant_wf itermSubtract_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_subtract_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf le_wf wellfounded_functionality_wrt_iff iff_weakening_uiff minus_mono_wrt_lt decidable__lt itermMinus_wf int_term_value_minus_lemma gt_wf all_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis intEquality dependent_functionElimination natural_numberEquality sqequalRule lambdaEquality setElimination rename dependent_set_memberEquality because_Cache productElimination unionElimination independent_isectElimination approximateComputation independent_functionElimination dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality independent_pairFormation minusEquality isect_memberFormation functionEquality applyEquality cumulativity universeEquality

Latex:
\mforall{}i:\mBbbZ{}.  \mforall{}j:\{i...\}.    WellFnd\{i\}(\{i..j\msupminus{}\};x,y.x  >  y)

Date html generated: 2018_05_21-PM-00_26_14
Last ObjectModification: 2018_05_19-AM-06_52_04

Theory : int_2

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