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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