### Nuprl Lemma : int_eq-sqle-lemma1

`∀[x:Top]. ∀[y:ℤ].  (if x=y then x else ⊥ ≤ x)`

Proof

Definitions occuring in Statement :  bottom: `⊥` uall: `∀[x:A]. B[x]` top: `Top` int_eq: `if a=b then c else d` int: `ℤ` sqle: `s ≤ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` has-value: `(a)↓` subtype_rel: `A ⊆r B` and: `P ∧ Q` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` uimplies: `b supposing a` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` false: `False` iff: `P `⇐⇒` Q` not: `¬A` rev_implies: `P `` Q` top: `Top`
Lemmas referenced :  int_subtype_base eq_int_wf eqtt_to_assert assert_of_eq_int has-value_wf_base is-exception_wf eqff_to_assert bool_subtype_base bool_cases_sqequal subtype_base_sq bool_wf iff_transitivity assert_wf bnot_wf not_wf equal-wf-base iff_weakening_uiff assert_of_bnot istype-assert istype-void bottom-sqle exception-not-value value-type-has-value int-value-type istype-int istype-top
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut sqleRule thin divergentSqle callbyvalueIntEq sqequalHypSubstitution hypothesis sqequalRule baseApply closedConclusion baseClosed hypothesisEquality applyEquality extract_by_obid productElimination isectElimination Error :inhabitedIsType,  Error :lambdaFormation_alt,  unionElimination equalityElimination because_Cache independent_isectElimination equalityTransitivity equalitySymmetry int_eqReduceTrueSq sqleReflexivity Error :dependent_pairFormation_alt,  Error :equalityIsType4,  promote_hyp dependent_functionElimination instantiate cumulativity independent_functionElimination voidElimination intEquality independent_pairFormation Error :functionIsType,  int_eqReduceFalseSq Error :isect_memberEquality_alt,  Error :equalityIsType1,  int_eqExceptionCases axiomSqleEquality exceptionSqequal Error :isectIsTypeImplies

Latex:
\mforall{}[x:Top].  \mforall{}[y:\mBbbZ{}].    (if  x=y  then  x  else  \mbot{}  \mleq{}  x)

Date html generated: 2019_06_20-AM-11_27_24
Last ObjectModification: 2018_10_27-AM-11_14_36

Theory : call!by!value_2

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