Nuprl Lemma : evalall-sqequal

`∀[x:Base]. evalall(x) ~ x supposing (evalall(x))↓`

Proof

Definitions occuring in Statement :  has-value: `(a)↓` evalall: `evalall(t)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` base: `Base` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` evalall: `evalall(t)` all: `∀x:A. B[x]` implies: `P `` Q` and: `P ∧ Q` subtype_rel: `A ⊆r B` nat: `ℕ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` prop: `ℙ` false: `False` ge: `i ≥ j ` guard: `{T}` has-value: `(a)↓` top: `Top` not: `¬A` nat_plus: `ℕ+` sq_type: `SQType(T)` or: `P ∨ Q` cand: `A c∧ B` outl: `outl(x)` outr: `outr(x)`
Lemmas referenced :  has-value_wf_base set_subtype_base le_wf int_subtype_base base_wf nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf fun_exp0_lemma istype-void strictness-apply bottom_diverge subtract-1-ge-0 nat_wf fun_exp_unroll_1 subtype_base_sq subtype_rel_self has-value-implies-dec-ispair-2 top_wf has-value-implies-dec-isinl-2 has-value-implies-dec-isinr-2
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut sqequalHypSubstitution sqequalRule hypothesis compactness thin baseClosed Error :inhabitedIsType,  Error :lambdaFormation_alt,  axiomSqEquality dependent_functionElimination hypothesisEquality independent_functionElimination productElimination Error :universeIsType,  extract_by_obid isectElimination baseApply closedConclusion applyEquality intEquality Error :lambdaEquality_alt,  natural_numberEquality independent_isectElimination Error :equalityIsType1,  equalityTransitivity equalitySymmetry Error :isect_memberEquality_alt,  Error :isectIsTypeImplies,  setElimination rename intWeakElimination voidElimination independent_pairEquality axiomSqleEquality Error :functionIsTypeImplies,  because_Cache Error :dependent_set_memberEquality_alt,  instantiate cumulativity promote_hyp callbyvalueCallbyvalue callbyvalueReduce unionElimination independent_pairFormation

Latex:
\mforall{}[x:Base].  evalall(x)  \msim{}  x  supposing  (evalall(x))\mdownarrow{}

Date html generated: 2019_06_20-PM-00_26_48
Last ObjectModification: 2018_10_15-PM-05_16_30

Theory : fun_1

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