### Nuprl Lemma : absval-sqequal-imax

`∀[a:Top]. (imax(a;-a) ~ |a|)`

Proof

Definitions occuring in Statement :  imax: `imax(a;b)` absval: `|i|` uall: `∀[x:A]. B[x]` top: `Top` minus: `-n` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` sq_type: `SQType(T)` all: `∀x:A. B[x]` implies: `P `` Q` guard: `{T}` absval: `|i|` imax: `imax(a;b)` has-value: `(a)↓` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` ifthenelse: `if b then t else f fi ` less_than: `a < b` less_than': `less_than'(a;b)` top: `Top` true: `True` squash: `↓T` not: `¬A` false: `False` prop: `ℙ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` bfalse: `ff` or: `P ∨ Q` bnot: `¬bb` assert: `↑b` le: `A ≤ B`
Lemmas referenced :  subtype_base_sq int_subtype_base value-type-has-value int-value-type le_int_wf eqtt_to_assert assert_of_le_int lt_int_wf bool_wf assert_of_lt_int top_wf less_than_wf satisfiable-full-omega-tt intformand_wf intformless_wf itermConstant_wf itermVar_wf intformle_wf itermMinus_wf int_formula_prop_and_lemma int_formula_prop_less_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_le_lemma int_term_value_minus_lemma int_formula_prop_wf eqff_to_assert equal_wf bool_cases_sqequal bool_subtype_base assert-bnot le_wf intformnot_wf int_formula_prop_not_lemma has-value_wf_base is-exception_wf exception-not-value
Rules used in proof :  cut sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction thin instantiate extract_by_obid sqequalHypSubstitution isectElimination cumulativity intEquality independent_isectElimination hypothesis dependent_functionElimination equalityTransitivity equalitySymmetry independent_functionElimination sqequalAxiom hypothesisEquality sqequalRule callbyvalueReduce because_Cache minusEquality lambdaFormation unionElimination equalityElimination productElimination natural_numberEquality lessCases isect_memberEquality independent_pairFormation voidElimination voidEquality imageMemberEquality baseClosed imageElimination dependent_pairFormation lambdaEquality int_eqEquality computeAll promote_hyp sqequalSqle sqleRule divergentSqle callbyvalueExceptionCases axiomSqleEquality exceptionSqequal sqleReflexivity baseApply closedConclusion callbyvalueCallbyvalue callbyvalueMinus minusExceptionCases callbyvalueLess lessExceptionCases

Latex:
\mforall{}[a:Top].  (imax(a;-a)  \msim{}  |a|)

Date html generated: 2017_04_14-AM-09_13_20
Last ObjectModification: 2017_02_27-PM-03_51_03

Theory : int_2

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